The problem of multiple-computations discovered by Hilary Putnam presents a deep difficulty for functionalism (of all sorts, computational and causal). We describe in out- line why Putnam’s result, and likewise the more restricted result we call the Multiple- Computations Theorem, are in fact theorems of statistical mechanics. We show why the mere interaction of a computing system with its environment cannot single out a computation as the preferred one amongst the many computations implemented by the system. We explain why nonreductive (...) approaches to solving the multiple- computations problem, and in particular why computational externalism, are dualistic in the sense that they imply that nonphysical facts in the environment of a computing system single out the computation. We discuss certain attempts to dissolve Putnam’s unrestricted result by appealing to systems with certain kinds of input and output states as a special case of computational externalism, and show why this approach is not workable without collapsing to behaviorism. We conclude with some remarks about the nonphysical nature of mainstream approaches to both statistical mechanics and the quantum theory of measurement with respect to the singling out of partitions and observables. (shrink)

This paper describes a version of type identity physicalism, which we call Flat Physicalism, and shows how it meets several objections often raised against identity theories. This identity theory is informed by recent results in the conceptual foundations of physics, and in particular clar- ifies the notion of ‘physical kinds’ in light of a conceptual analysis of the paradigmatic case of reducing thermody- namics to statistical mechanics. We show how Flat Physi- calism is compatible with the appearance of multiple realisation (...) in the special sciences, and how and in what sense the special sciences laws are autonomous from the laws of physics, despite the full reductive picture of Flat Physicalism. We compare our view with a recent proposal by William Bechtel that accounts for the appearance of levels in mechanistic explanations. (shrink)

It is often said that the world is explained by laws of nature together with initial conditions. But does that mean initial conditions don’t require further explanation? And does the explanatory role played by initial conditions entail or require that time has a preferred direction? This chapter looks at the use of the ‘initialness defence’ in physics, the idea that initial conditions are intrinsically special in that they don’t require further explanation, unlike the state of the world at other times. (...) Such defences commonly assume a primitive directionality of time to distinguish between initial and final conditions. Using the case study of the time-asymmetry of thermodynamics and the so-called ‘past hypothesis’ — the hypothesis that the early universe was in a state of very low entropy —, I outline and support a deflationary account of the initialness defence that does not pre- suppose a basic directionality of time, and argue that there is a relevant explanatory asymmetry between initial conditions and the state of systems at other times only if certain causal conditions are satisfied. Hence, the initialness defence is available to those who reject a fundamental direction of time. (shrink)

According to the free energy principle, life is an “inevitable and emergent property of any random dynamical system at non-equilibrium steady state that possesses a Markov blanket” :20130475, 2013). Formulating a principle for the life sciences in terms of concepts from statistical physics, such as random dynamical system, non-equilibrium steady state and ergodicity, places substantial constraints on the theoretical and empirical study of biological systems. Thus far, however, the physics foundations of the free energy principle have received hardly any attention. (...) Here, we start to fill this gap and analyse some of the challenges raised by applications of statistical physics for modelling biological targets. Based on our analysis, we conclude that model-building grounded in the free energy principle exacerbates a trade-off between generality and realism, because of a fundamental mismatch between its physics assumptions and the properties of actual biological targets. (shrink)

En esta entrada se mencionan las principales cuestiones en los fundamentos de la mecánica estadı́stica y la termodinámica, y las cuestiones filosóficas en las que repercuten estas áreas de la fı́sica. Al final se añaden lecturas recomendadas, enfatizando las traducidas al español.

I will argue, pace a great many of my contemporaries, that there's something right about Boltzmann's attempt to ground the second law of thermodynamics in a suitably amended deterministic time-reversal invariant classical dynamics, and that in order to appreciate what's right about (what was at least at one time) Boltzmann's explanatory project, one has to fully apprehend the nature of microphysical causal structure, time-reversal invariance, and the relationship between Boltzmann entropy and the work of Rudolf Clausius.

We present a novel reductive theory of type-identity physicalism, which is inspired by the foundations of statistical mechanics as a general theory of natural kinds. We show that all the claims mounted against type-identity physicalism in the literature don’t apply to Flat Physicalism, and moreover that this reductive theory solves many of the problems faced by the various non-reductive approaches including functionalism. In particular, we show that Flat Physicalism can account for the appearance of multiple realizability in the special sciences, (...) and that it gives a novel account of the genuine autonomy of the kinds and laws in the special sciences. We further show that the thesis of genuine multiple realization, which is compatible with all forms of non-reductive approaches including functionalism, implies what we call token-dualism; namely the idea that in every token there are non-physical facts, which may either be non-physical properties or some non-physical substance. In other words, we prove that non-reductive kinds necessarily assume non-reductive tokens, i.e., token dualism. Finally, we show that all forms of non-reductive approaches including functionalism imply a literally multi-leveled structure of reality. (shrink)

Philosophers of physics have long debated whether the Past State of low entropy of our universe calls for explanation. What is meant by “calls for explanation”? In this article we analyze this notion, distinguishing between several possible meanings that may be attached to it. Taking the debate around the Past State as a case study, we show how our analysis of what “calling for explanation” might mean can contribute to clarifying the debate and perhaps to settling it, thus demonstrating the (...) fruitfulness of this analysis. Applying our analysis, we show that two main opponents in this debate, Huw Price and Craig Callender, are, for the most part, talking past each other rather than disagreeing, as they employ different notions of “calling for explanation”. We then proceed to show how answering the different questions that arise out of the different meanings of “calling for explanation” can result in clarifying the problems at hand and thus, hopefully, to solving them. (shrink)

There are two theoretical approaches in statistical mechanics, one associated with Boltzmann and the other with Gibbs. The theoretical apparatus of the two approaches offer distinct descriptions of the same physical system with no obvious way to translate the concepts of one formalism into those of the other. This raises the question of the status of one approach vis-à-vis the other. We answer this question by arguing that the Boltzmannian approach is a fundamental theory while Gibbsian statistical mechanics is an (...) effective theory, and we describe circumstances under which Gibbsian calculations coincide with the Boltzmannian results. We then point out that regarding GSM as an effective theory has important repercussions for a number of projects, in particular attempts to turn GSM into a nonequilibrium theory. (shrink)

This paper makes a novel linkage between the multiple-computations theorem in philosophy of mind and Landauer’s principle in physics. The multiple-computations theorem implies that certain physical systems implement simultaneously more than one computation. Landauer’s principle implies that the physical implementation of “logically irreversible” functions is accompanied by minimal entropy increase. We show that the multiple-computations theorem is incompatible with, or at least challenges, the universal validity of Landauer’s principle. To this end we provide accounts of both ideas in terms of (...) low-level fundamental concepts in statistical mechanics, thus providing a deeper understanding of these ideas than their standard formulations given in the high-level terms of thermodynamics and cognitive science. Since Landauer’s principle is pivotal in the attempts to derive the universal validity of the second law of thermodynamics in statistical mechanics, our result entails that the multiple-computations theorem has crucial implications with respect to the second law. Finally, our analysis contributes to the understanding of notions, such as “logical irreversibility,” “entropy increase,” “implementing a computation,” in terms of fundamental physics, and to resolving open questions in the literature of both fields, such as: what could it possibly mean that a certain physical process implements a certain computation. (shrink)

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology (...) and to the quantum measurement problem. (shrink)

The relationship between statistical mechanics and population genetics has a long history. Both take advantage of statistics to address the behavior of large groups of entities. The main objective of this article is to assess the obstacles population genetics is meeting in its claim to explain biological phenomena from the conceptual apparatus of statistical mechanics according to two recent articles. Several tools available to the latter are missing in the former. Thus, in the absence of an adequate justification of the (...) relevance of the analogy and without the satisfaction of certain basic assumptions, I argue that the explanatory strategy of the analogously based model is seriously compromised. La relation entre mécanique statistique et génétique des populations a une longue histoire. À l’instar de la première, la seconde tire profit des statistiques afin de traiter le comportement des grands ensembles d’entités. L’objectif principal du présent article est d’identifier les obstacles que rencontre la génétique des populations dans sa prétention d’explication des phénomènes biologiques à partir de l’appareillage conceptuel de la mécanique statistique selon deux articles récents. Or, plusieurs outils dont dispose cette dernière manque à la première. Ainsi, en l’absence d’une justification adéquate de la pertinence de l’analogie et sans la satisfaction de certaines hypothèses fondamentales, je soutiens que la stratégie explicative du modèle analogue est sérieusement compromise. (shrink)

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests (...) interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics. (shrink)

Statistical mechanics is a strange theory. Its aims are debated, its methods are contested, its main claims have never been fully proven, and their very truth is challenged, yet at the same time, it enjoys huge empirical success and gives us the feeling that we understand important phenomena. What is this weird theory, exactly? Statistical mechanics is the name of the ongoing attempt to apply mechanics, together with some auxiliary hypotheses, to explain and predict certain phenomena, above all those described (...) by thermodynamics. This paper shows what parts of this objective can be achieved with mechanics by itself. It thus clarifies what roles remain for the auxiliary assumptions that are needed to achieve the rest of the desiderata. Those auxiliary hypotheses are described in another paper in this journal, Foundations of statistical mechanics: The auxiliary hypotheses. (shrink)

Statistical mechanics is the name of the ongoing attempt to explain and predict certain phenomena, above all those described by thermodynamics on the basis of the fundamental theories of physics, in particular mechanics, together with certain auxiliary assumptions. In another paper in this journal, Foundations of statistical mechanics: Mechanics by itself, I have shown that some of the thermodynamic regularities, including the probabilistic ones, can be described in terms of mechanics by itself. But in order to prove those regularities, in (...) particular the time asymmetric ones, it is necessary to add to mechanics assumptions of three kinds, all of which are under debate in contemporary literature. One kind of assumptions concerns measure and probability, and here, a major debate is around the notion of “typicality.” A second assumption concerns initial conditions, and here, the debate is about the nature and status of the so-called past hypothesis. The third kind of assumptions concerns the dynamics, and here, the possibility and significance of “Maxwell's Demon” is the main topic of discussions. This article describes these assumptions and examines the justification for introducing them, emphasizing the contemporary debates around them. (shrink)

I discuss the formal implementation, interpretation, and justification of likelihood attributions in cosmology. I show that likelihood arguments in cosmology suffer from significant conceptual and formal problems that undermine their applicability in this context.

Despite of its formal precision and its great many applications, Shannon’s theory still offers an active terrain of debate when the interpretation of its main concepts is the task at issue. In this article we try to analyze certain points that still remain obscure or matter of discussion, and whose elucidation contribute to the assessment of the different interpretative proposals about the concept of information. In particular, we argue for a pluralist position, according to which the different views about information (...) are no longer rival, but different interpretations of a single formal concept. (shrink)

We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)

This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on (...) and summarize the highlights of the individual contributions. (shrink)

Special sciences (such as biology, psychology, economics) describe various regularities holding at some high macroscopic level. One of the central questions concerning these macroscopic regularities is how they are related to the laws of physics governing the underlying microscopic physical reality. In this paper we show how a macroscopic regularity may emerge from an underlying micro- scopic structure, and how the appearance of multiple realizability of the special sciences by physics comes about in a reductionist-physicalist framework. On this basis we (...) explain how complexity at the high level can arise due to a sort of harmony between the microscopic dynamics and observer-dependent macroscopic properties. We show that observer-dependent properties, which underlie the emergence of macroscopic properties and of macroscopic complexity, are objective physical facts. We argue that such physical properties remove the mystery from the multiple realizability of special sciences’ kinds, since the latter are grounded in shared physical properties. Finally we explain how and in what sense in our reductive physicalist approach the special sciences are still autonomous after all. (shrink)

Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to the largest (...) macro-region. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. (shrink)

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.

In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...) theories and their logical relations is entirely inadequate with respect to what is going on in actual biological research practice. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...) to statistical mechanical probabilities. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The second of these articles discusses the regularity approach to statistical mechanical probabilities, and describes some areas (...) where further research is needed. (shrink)

We start by very briefly describing the measurement problem in quantum mechanics and its solution by the Many Worlds Interpretation. We then describe the preferred basis problem, and the role of decoherence in the MWI. We discuss a number of approaches to the preferred basis problem and argue that contrary to the received wisdom, decoherence by itself does not solve the problem. We address Wallace’s emergentist approach based on what he calls Dennett’s criterion, and we compare the logical structure of (...) Wallace’s argument that the Hilbert space structure and the unitary dynamics should be considered a complete description of the physics of the universe with the logical structure of the EPR argument against the completeness of quantum mechanics. Then, we consider the nature of so-called “high level emergent facts” and Dennett’s criterion in Wallace’s approach and we discuss the implications of its non-reductive nature. Finally, we conclude that the MWI is not a straightforward interpretation of pure quantum mechanics that doesn't add anything to it. Whether or not it is more parsimonious than other quantum mechanical theories depends on the details of the additions. (shrink)

Can Brownian motion arise from a deterministic system of particles? This paper addresses this question by analysing the derivation of Brownian motion as the limit of a deterministic hard-spheres gas with Lanford’s theorem. In particular, we examine the role of the Boltzmann-Grad limit in the loss of memory of the deterministic system and compare this derivation and the derivation of Brownian motion with the Langevin equation.

Is freedom compatible with determinism? Davidson famously rephrased this question by replacing “freedom” with “anomaly of the mental”, that is, failure to fall under a law. In order to prove that the anomaly of the mental is compatible with other conjectures he makes, in particular that: there is psycho-physical causation; “where there is causality, there must be a law” ; and the mental supervenes on the physical, Davidson proposed a model, that came to be known as anomalous monism. Accepting all (...) of Davidson’s conjectures, we compare the structure of Davidson’s argument with that of Einstein’s argument for the special theory of relativity. This leads us to an exposition of Davidson’s ontology in terms that are inspired by recent results in the philosophy of physics, that is, in terms of fundamental ontology and high-level coarse-grained descriptions. We explain in what sense Davidson’s model is a principle theory and discuss some requirements that the constructive theory underlying Davidson's principle approach must satisfy. We propose two constructive theories of description that may underlie Davidson's approach and this deeper structure leads us to formulating a dilemma according to which Davidson's approach entails either a non-physicalist type-identity reductive and monistic structure of events; or else it entails a structure of events that requires what we call token-substance dualism. We consider some issues which seem to suggest that the first horn of this dilemma collapses into a reductive type-identity physicalist theory, contrary to Davidson's intent. Finally, we show how Davidson's achievement of accounting for some freedom of the mental from the physical and the anomaly of the mental within anomalous monism can be achieved in a fully reductive type-identity physicalist theory. (shrink)

There is a longstanding debate on the metaphysical relation between quantum states and the systems they describe. A series of relatively recent ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-ontology theorems have been taken to show that, provided one accepts certain assumptions, “quantum states are real”. In this paper I investigate the question of what that claim might be taken to mean in light of these theorems. It is argued that, even if one accepts the framework and assumptions (...) employed by such theorems, such a conclusion is not warranted. Specifically, I argue that when a so-called ontic state is taken to describe the properties of a system, the relation between this state and some quantum state as established by ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-ontology theorems, is not of the kind that would warrant counting the quantum state among these properties in any way. (shrink)

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a 'typical' dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light --a different light-- on philosophical debates on the laws of (...) nature. In the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The conditions required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such conditions might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

In this paper I will defend the incapacity of the informational frameworks in thermal physics, mainly those that historically and conceptually derive from the work of Brillouin (1962) and Jaynes (1957a), to robustly explain the approach of certain gaseous systems to their state of thermal equilibrium from the dynamics of their molecular components. I will further argue that, since their various interpretative, conceptual and technical-formal resources (e.g. epistemic interpretations of probabilities and entropy measures, identification of thermal entropy as Shannon information, (...) and so on) are shown to be somehow incoherent, inconsistent or inaccurate, these informational proposals need to 'epistemically parasitize' the manifold of theoretical resources of Boltzmann's and Gibbs' statistical mechanics, respectively, in order to properly account for the equilibration process of an ideal gas from its microscopic properties. Finally, our conclusion leads us to adopt a sort of constructive skepticism regarding the explanatory value of the main informationalist trends in statistical thermophysics. (shrink)

Must a theory of quantum gravity have some truth to it if it can recover general relativity in some limit of the theory? This paper answers this question in the negative by indicating that general relativity is multiply realizable in quantum gravity. The argument is inspired by spacetime functionalism—multiple realizability being a central tenet of functionalism—and proceeds via three case studies: induced gravity, thermodynamic gravity, and entanglement gravity. In these, general relativity in the form of the Einstein field equations can (...) be recovered from elements that are either manifestly multiply realizable or at least of the generic nature that is suggestive of functions. If general relativity, as argued here, can inherit this multiple realizability, then a theory of quantum gravity can recover general relativity while being completely wrong about the posited microstructure. As a consequence, the recovery of general relativity cannot serve as the ultimate arbiter that decides which theory of quantum gravity that is worthy of pursuit, even though it is of course not irrelevant either qua quantum gravity. Thus, the recovery of general relativity in string theory, for instance, does not guarantee that the stringy account of the world is on the right track; despite sentiments to the contrary among string theorists. (shrink)

In his mature writings, Kuhn describes the process of specialisation as driven by a form of incommensurability, defined as a conceptual/linguistic barrier which promotes and guarantees the insularity of specialties. In this paper, we reject the idea that the incommensurability among scientific specialties is a linguistic barrier. We argue that the problem with Kuhn’s characterisation of the incommensurability among specialties is that he presupposes a rather abstract theory of semantic incommensurability, which he then tries to apply to his description of (...) the process of specialisation. By contrast, this paper follows a different strategy: after criticising Kuhn’s view, it takes a further look at how new scientific specialties emerge. As a result, a different way of understanding incommensurability among specialties will be proposed. (shrink)

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-epsilon-equilibrium. This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic systems equilibrium macro-regions are large in requisite sense.

While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics, progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced much criticism. I (...) focus on two objections in the literature: claims that coarse-graining makes time-asymmetry ‘illusory’ and ‘anthropocentric’. I argue that these objections arise from an unsatisfactory justification of coarse-graining prevalent in the literature, rather than from coarse-graining itself. This justification relies on the idea of measurement imprecision. By considering the role that abstraction and autonomy play, I provide an alternative justification and offer replies to the illusory and anthropocentric objections. Finally, I consider the broader consequences of this alternative justification: the connection to debates about inter-theoretic reduction and the implication that the time-asymmetry in SM is weakly emergent. 1Introduction 1.1Prospectus2The Zwanzig–Zeh–Wallace Framework3Why Does This Method Work? 3.1The special conditions account3.2When is a density forwards-compatible?4Anthropocentrism and Illusion: Two Objections 4.1The two objections in more detail4.2Against the justification by measurement imprecision5An Alternative Justification 5.1Abstraction and autonomy5.2An illustration: the Game of Life6Reply to Illusory7Reply to Anthropocentric8The Wider Landscape: Concluding Remarks 8.1Inter-theoretic relations8.2The nature of irreversibility. (shrink)

There are two main theoretical frameworks in statistical mechanics, one associated with Boltzmann and the other with Gibbs. Despite their well-known differences, there is a prevailing view that equilibrium values calculated in both frameworks coincide. We show that this is wrong. There are important cases in which the Boltzmannian and Gibbsian equilibrium concepts yield different outcomes. Furthermore, the conditions under which equilibriums exists are different for Gibbsian and Boltzmannian statistical mechanics. There are, however, special circumstances under which it is true (...) that the equilibrium values coincide. We prove a new theorem providing sufficient conditions for this to be the case. (shrink)

This thesis makes the issue of reconciling the existence of thermodynamically irreversible processes with underlying reversible dynamics clear, so as to help explain what philosophers mean when they say that an aim of nonequilibrium statistical mechanics is to underpin aspects of thermodynamics. Many of the leading attempts to reconcile the existence of thermodynamically irreversible processes with underlying reversible dynamics proceed by way of discussions that attempt to underpin the following qualitative facts: (i) that isolated macroscopic systems that begin away from (...) equilibrium spontaneously approach equilibrium, and (ii) that they remain in equilibrium for incredibly long periods of time. These attempts standardly appeal to phase space considerations and notions of typicality. This thesis considers and evaluates leading typicality accounts, and, in particular, highlights their limitations. Importantly, these accounts do not underpin a large and important set of facts. They do not, for example, underpin facts about the rates in which systems approach equilibrium, or facts about the kinds of states they pass through on their way to equilibrium, or facts about fluctuation phenomena. To remedy these and other shortfalls, this thesis promotes an alternative, and arguably more important, line of research: understanding and accounting for the success of the techniques and equations physicists use to model the behaviour of systems that begin away from equilibrium. Accounting for their success would help underpin not just the qualitative facts the literature has focused on, but also many of the important quantitative facts that typicality accounts cannot. This thesis also takes steps in this promising direction. It outlines and examines a technique commonly used to model the behaviour of an interesting and important kind of system: a Brownian particle that's been introduced to an isolated homogeneous fluid at equilibrium. As this thesis highlights, the technique returns a wealth of quantitative and qualitative information. This thesis also attempts to account for the success of the model and technique, by identifying and grounding the technique's key assumptions. (shrink)

Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. We (...) then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence. (shrink)

In our book The Road to Maxwell’s Demon (RMD) (Cambridge University Press 2012) we proposed a new outline for a reductive account of statistical mechanics in which thermodynamics is reduced to classical mechanics. In a recent review Valia Allori says that we misunderstood Boltzmann’s account of statistical mechanics with respect to two issues: (1) the nature of typicality considerations in Boltzmann’s explanation of the Second Law - and here she provides no argument whatsoever; and (2) Boltzmann’s notion of probability. As (...) to the second issue, unfortunately, there are flaws in her presentation of Boltzmann’s work as well as of ours. In this paper we briefly explain the difference between Boltzmann’s notion of probability and our notion, how the latter in fact complements Boltzmann’s ideas, and Allori’s flaws on these issues. (shrink)

Probability and indeterminism have always been core philosophical themes. This paper aims to contribute to understanding probability and indeterminism in biology. To provide the background for the paper, it will first be argued that an omniscient being would not need the probabilities of evolutionary theory to make predictions about biological processes. However, despite this, one can still be a realist about evolutionary theory, and then the probabilities in evolutionary theory refer to real features of the world. This prompts the question (...) of how to interpret biological probabilities which correspond to real features of the world but are in principle dispensable for predictive purposes. This paper will suggest three possible interpretations. The first interpretation is a propensity interpretation of kinds of systems. It will be argued that backward probabilities in biology do not present a problem for this propensity interpretation. The second interpretation is the frequency interpretation. Third, I will suggest Humean chances are a new interpretation of probability in evolutionary theory. Finally, this paper discusses Sansom’s argument that biological processes are indeterministic because probabilities in evolutionary theory refer to real features of the world. It will be argued that Sansom’s argument is not conclusive, and that the question whether biological processes are deterministic or indeterministic is still with us. (shrink)

Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart. Despite many ‘proofs of concept’ (Aharonov and Ben–Or 1996; Knill and Laflamme 1996; Knill et al. 1996; Knill et al. 1998) the key obstacle in realizing these powerful machines remains their scalability and susceptibility to noise: almost three decades after their conceptions, experimentalists (...) still struggle to maintain useful quantum coherence in QIP devices with more than a pair of qubits (e.g., Blatt and Wineland 2008). This slow progress has prompted debates on the feasibility of quantum computers, yet the quantum information community has dismissed the skepticism as “ideology” (Aaronson 2004), claiming that the obstacles are merely technological (Kaye et al. 2007, 240). In a recent paper (Hagar 2009) I’ve argued that such a skepticism with respect to the feasibility of quantum computers need not be deemed ideological at all, and that the aforementioned ‘proofs of concept’ are physically suspect. Using analogies from the foundations of classical statistical mechanics (SM), I’ve also argued that instead of active error correction, the appropriate framework for debating the feasibility of large–scale, fault–tolerant and computationally superior quantum computers should be the project of error avoidance: rather than trying to constantly ‘cool down’ the QIP device and prevent its thermalization, one should try to locate those regions in the device’s state space which are thermodynamically ‘abnormal’, i.e., those regions in the device’s state space which resist thermalization regardless of external noise. This paper is intended as a further contribution to the debate on the feasibility of large–scale, fault–tolerant and computationally superior quantum computers. Relying again on analogies from the foundations of classical SM, it suggests a skeptical conjecture and frames it in the ‘passive’, error avoidance, context.. (shrink)

Let us begin with a characteristic example. Consider a gas that is confined to the left half of a box. Now we remove the barrier separating the two halves of the box. As a result, the gas quickly disperses, and it continues to do so until it homogeneously fills the entire box. This is illustrated in Figure 1.

This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of (...) reduction and emergence. (shrink)

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it (...) explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation. (shrink)

We reconsider the Nagelian theory of reduction and argue that, contrary to a widely held view, it is the right analysis of intertheoretic reduction. The alleged difficulties of the theory either vanish upon closer inspection or turn out to be substantive philosophical questions rather than knock-down arguments.

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations (...) of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (shrink)

The thesis proposes, defends, and applies a new model of inter-theoretic reduction, called "Neo-Nagelian" reduction. There are numerous accounts of inter-theoretic reduction in the philosophy of science literature but the most well-known and widely-discussed is the Nagelian one. In the thesis I identify various kinds of problems which the Nagelian model faces. Whilst some of these can be resolved, pressing ones remain. In lieu of the Nagelian model, other models of inter-theoretic reduction have been proposed, chief amongst which are so-called (...) "New Wave" models. I show these to be no more adequate than the original Nagelian model. I propose a new model of inter-theoretic reduction, Neo-Nagelian reduction. This model is structurally similar to the Nagelian one, but differs in substantive ways. In particular I argue that it avoids the problems pertaining to both the Nagelian and New Wave models. Multiple realizability looms large in discussions about reduction: it is claimed that multiply realizable properties frustrate the reduction of one theory to another in various ways. I consider these arguments and show that they do not undermine the Neo-Nagelian of reduction of one theory to another. Finally, I apply the model to statistical mechanics. Statistical mechanics is taken to be a reductionist enterprise: one of the aims of statistical mechanics is to reduce thermodynamics. Without an adequate model of inter-theoretic reduction one cannot assess whether it succeeds; I use the Neo-Nagelian model to critically discuss whether it does. Specifically, I consider two very recent derivations of the Second Law of thermodynamics, one from Boltzmannian classical statistical mechanics and another from quantum statistical mechanics. I argue that they are partially successful, and that each makes for a promising line of future research. (shrink)