The thermodynamics of computation assumes that computational processes at the molecular level can be brought arbitrarily close to thermodynamic reversibility and that thermodynamic entropy creation is unavoidable only in data erasure or the merging of computational paths, in accord with Landauer’s principle. The no-go result shows that fluctuations preclude completion of thermodynamically reversible processes. Completion can be achieved only by irreversible processes that create thermodynamic entropy in excess of the Landauer limit.

We discuss a recent proposal by Albert (1994a; 1994b; 2000, ch. 7) to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wave function by Ghirardi, Rimini, and Weber (1986). We propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies on the standard quantum mechanical models of environmental decoherence of open systems (e.g., Joos and Zeh 1985; Zurek and Paz 1994). This paper presents the two approaches (...) and discusses their advantages. The problems faced by both approaches will be discussed in a sequel (Hemmo and Shenker 2003). (shrink)

Scientists investigating the thermal properties of black holes rely heavily on theoretical and non-empirical tools, such as mathematical derivations, analogue experiments and thought experiments. Although the use of mathematical derivations and analogue experiments in the context of black hole physics has recently received a great deal of attention among philosophers of science, the use of thought experiments (TEs) in that context has been almost completely neglected. In this paper, we will start filling this gap by systematically analyzing the epistemic role (...) of the two TEs that gave birth to black hole thermodynamics, namely Wheeler’s demon and Geroch’s engine. We will argue that the two main epistemic functions of these TEs are to reveal and resolve inconsistencies, in line with El Skaf’s (Probing theoretical statements with thought experiments. Synthese 199:6119–6147, 2021) approach to TEs. We will, then, go beyond El Skaf’s approach by stressing an important difference between the strategies employed to assess the reliability of each epistemic function. (shrink)

Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Hemmo and Shenker (2006) have recently argued against this view by attacking von Neumann's (1955) argument. I argue that Hemmo and Shenker's arguments fail due to several misunderstandings: about statistical-mechanical and thermodynamic domains of applicability, about the nature of mixed states, and about the role of approximations in physics. As a result, their arguments fail in all cases: in the single-particle case, the finite particles case, and the (...) infinite particles case. (shrink)

Information, entropy, probability: these three terms are closely interconnected in the prevalent understanding of statistical mechanics, both when this field is taught to students at an introductory level and in advanced research into the field’s foundations. This paper examines the interconnection between these three notions in light of recent research in the foundations of statistical mechanics. It disentangles these concepts and highlights their differences, at the same time explaining why they came to be so closely linked in the literature. In (...) the literature the term ‘information’ is often linked to entropy and probability in discussions of Maxwell’s Demon and its attempted exorcism by the Landauer-Bennett thesis, and in analyses of the spin echo experiments. The direction taken in the present paper is a different one. Here we discuss the statistical mechanical underpinning of the notions of probability and entropy, and this constructive approach shows that information plays no fundamental role in these concepts, although it can be conveniently used in a sense that we shall specify. (shrink)

The argument from causal closure of the physical is usually considered the most powerful argument in favor of the ontological doctrine of physicalism. Many authors, most notably Papineau, assume that CCP implies that physicalism is supported by physics. I demonstrate, however, that physical science has no bias in the ontological debate between proponents of physicalism and dualism. I show that the arguments offered for CCP are effective only against the accounts of mental causation based on the action of the mental (...) forces of a Newtonian nature, i.e. those which manifest themselves by causing accelerations. However, it is conceivable and possible that mental causation is manifested through the redistribution of energy, momentum and other conserved quantities in the system, brought about by altering the state probability distribution within the living system and leading to anomalous correlations of neural processes. After arguing that a probabilistic, interactionist model of mental causation is conceivable, which renders the argument from causal closure of the physical ineffective, I point to some basic features that such a model must have in order to be intelligible. At the same time, I indicate the way that conclusive testing of CCP can be done within the theoretical framework of physics. (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)

One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way that they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a probabilistic (...) one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his concept of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concepts that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover. (shrink)

Landauer’s principle is the loosely formulated notion that the erasure of n bits of information must always incur a cost of k ln n in thermodynamic entropy. It can be formulated as a precise result in statistical mechanics, but for a restricted class of erasure processes that use a thermodynamically irreversible phase space expansion, which is the real origin of the law’s entropy cost and whose necessity has not been demonstrated. General arguments that purport to establish the unconditional validity of (...) the law fail. They turn out to depend on the illicit formation of a canonical ensemble from memory devices holding random data. To exorcise Maxwell’s demon one must show that all candidate devices—the ordinary and the extraordinary—must fail to reverse the second law of thermodynamics. The theorizing surrounding Landauer’s principle is too fragile and too tied to a few specific examples to support such general exorcism. Charles Bennett’s recent extension of Landauer’s principle to the merging of computational paths fails for the same reasons as trouble the original principle. (shrink)

This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still made in subtle ways, the article explores its occurrence in three examples: the Second Law, the concept of equilibrium and the definition of phase transitions.

In a previous article, we have demonstrated by a general phase space argument that a Maxwellian Demon is compatible with statistical mechanics. In this article, we show how this idea can be put to work in the prevalent model of the Demon, namely, a particle-in-a-box, used, for example, by Szilard and Bennett. In the literature, this model is used in order to show that a Demon is incompatible with statistical mechanics, either classical or quantum. However, we show that a detailed (...) phase space analysis of this model illustrates that a Maxwellian Demon is compatible with statistical mechanics. (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)

Landauer’s principle is, roughly, the principle that logically irreversible operations cannot be performed without dissipation of energy, with a specified lower bound on that dissipation. Although widely accepted in the literature on the thermodynamics of computation, it has been the subject of considerable dispute in the philosophical literature. Proofs of the principle have been questioned on the grounds of insufficient generality and on the grounds of the assumption, used in the proofs, of the availability of reversible processes at the microscale. (...) The relevance of the principle, should it be true, has also been questioned, as it has been argued that microscale fluctuations entail dissipation that always greatly exceeds the Landauer bound. In this article Landauer’s principle is treated within statistical mechanics, and a proof of the principle is given that neither relies on neglect of fluctuations nor assumes the availability of thermodynamically reversible processes. In addition, it is argued that microscale fluctuations are no obstacle to approximating thermodynamic reversibility, in the appropriate sense, as closely as one would like. (shrink)

We show that the so-called Multiple-Computations Theorem in cognitive science and philosophy of mind challenges Landauer’s Principle in physics. Since the orthodox wisdom in statistical physics is that Landauer’s Principle is implied by, or is the mechanical equivalent of, the Second Law of thermodynamics, our argument shows that the Multiple-Computations Theorem challenges the universal validity of the Second Law of thermodynamics itself. We construct two examples of computations carried out by one and the same dynamical process with respect to which (...) Landauer’s principle implies contradictory predictions concerning the entropy increase. Our two examples are based on a weak version of the Multiple-Computations Theorem, which is quite uncontroversial, and therefore they amount to a clear refutation of the universal validity of Landauer’s Principle. We consider some responses to this argument that do not attempt to single out one computation over the others, and we show that they do not work. We further consider ways out of the argument by externalist approaches supporting the computational theory of the mind who propose that the interaction of a computing system with the environment is enough to select a single computation over the others. We show on physical grounds that this approach fails too. We then reverse the direction of our challenge and formulate a dilemma for supporters of the computational theory of the mind: they must reject the causal closure of physic; or else they must accept on a priori grounds that Landauer’s Principle and the Second Law of thermodynamics are not universally valid. Finally, we present our version of a type–type mind-brain identity theory called Flat Physicalism, which is based on the paradigm case of statistical mechanics, and we show that it circumvents the challenge from Landauer’s Principle and the Multiple-Computations Theorem and does not fall prey to our dilemma. (shrink)

Landauer's Principle asserts that there is an unavoidable cost in thermodynamic entropy creation when data is erased. It is usually derived from incorrect assumptions, most notably, that erasure must compress the phase space of a memory device or that thermodynamic entropy arises from the probabilistic uncertainty of random data. Recent work seeks to prove Landauer’s Principle without using these assumptions. I show that the processes assumed in the proof, and in the thermodynamics of computation more generally, can be combined to (...) produce devices that both violate the second law and erase data without entropy cost, indicating an inconsistency in the theoretical system. Worse, the standard repertoire of processes selectively neglects thermal fluctuations. Concrete proposals for how we might measure dissipationlessly and expand single molecule gases reversibly are shown to be fatally disrupted by fluctuations. Reversible, isothermal processes on molecular scales are shown to be disrupted by fluctuations that can only be overcome by introducing entropy creating, dissipative processes. (shrink)

. The origin and history of Landauer’s principle is traced through the development of the thermodynamics of computation at IBM from 1959 to 1982. This development was characterized by multiple conceptual shifts: memory came to be seen not as information storage, but as delayed information transmission; information itself was seen not as a disembodied logical entity, but as participating in the physical world; and logical irreversibility was connected with physical, thermodynamic, irreversibility. These conceptual shifts were characterized by an ambivalence opposing (...) strong metaphysical claims to practical considerations. Three sorts of practical considerations are discussed. First, these conceptual shifts engaged materials central to IBM’s business practice. Second, arguments for metaphysical certainties were made with reference to the practical functioning of typical computers. Third, arguments for metaphysical certainties were made in the context of establishing the thermodynamics of information as a sub-discipline of physics. (shrink)

The distribution function associated with a classical gas at equilibrium is considered. We prove that apart from a factorisable multiplier, the distribution function is fully determined by the correlations among local momenta fluctuations. Using this result we discuss the conditions which enable idealised local observers, who are immersed in the gas and form a part of it, to determine the distribution 'from within'. This analysis sheds light on two views on thermodynamic equilibrium, the 'ergodic' and the 'thermodynamic limit' schools, and (...) the relations between them. It also provides an outline for a new definition of equilibrium that is weaker than full ergodicity. Finally, we briefly discuss the possibility that the distribution can be determined by external observers. (shrink)

Kevin Davey claims that the justification of the second law of thermodynamics as it is conveyed by the “standard story” of statistical mechanics, roughly speaking, that lowentropy microstates tend to evolve to high-entropy microstates, is “unhelpful at best and wrong at worst.” In reply, I demonstrate that Davey’s argument for rejecting the standard story commits him to a form of skepticism that is more radical than the position he claims to be stating and that Davey places unreasonable demands on the (...) notion of justification in the physical sciences. (shrink)

There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics, but as a theory of how manipulations of a physical system may be used to obtain desired effects, such as mechanical work. On this view, the basic concepts of thermodynamics, heat and work, and with them, the concept of entropy, are relative to a class of envisaged manipulations. This article is a sketch and defense of a science of manipulations and their effects on physical (...) systems. I call this science thermo-dynamics, or ΘΔcs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta \Delta }^{\text{cs}}$$\end{document}, for short, to highlight that it may be different from the science of thermodynamics, as the reader conceives it. An upshot of the discussion is a clarification of the roles of the Gibbs and von Neumann entropies. Light is also shed on the use of coarse-grained entropies. (shrink)

It is generally accepted, following Landauer and Bennett, that the process of measurement involves no minimum entropy cost, but the erasure of information in resetting the memory register of a computer to zero requires dissipating heat into the environment. This thesis has been challenged recently in a two-part article by Earman and Norton. I review some relevant observations in the thermodynamics of computation and argue that Earman and Norton are mistaken: there is in principle no entropy cost to the acquisition (...) of information, but the destruction of information does involve an irreducible entropy cost. (shrink)

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: The erasure of one bit of information in a computational device is necessarily accompanied by a generation of kTln2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. John Norton (2005) and Owen Maroney (2005) both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers (...) a method that he claims instantiates the operation Reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences (assuming the second law of thermodynamics). We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'Reset', and thereby recover the quantitative form of Landauer's Principle. (shrink)

Special relativity is said to prohibit faster-than-light (superluminal) signaling, yet controversy regularly arises as to whether this or that physical phenomenon violates the prohibition. I argue that the controversy is a result of a lack of clarity as to what it means to ‘signal’, and I propose a criterion. I show that according to this criterion, superluminal signaling is not prohibited by special relativity.

Computer simulation (CS) and thought experiments (TE) seem to produce knowledge about the world without intervening in the world. This has called for a comparison between the two methods. However, Chandrasekharan et al. (2013) argue that the nature of contemporary science is too complex for using TEs. They suggest CS as the tool for contemporary sciences and conclude that it will replace TEs. In this paper, by discussing a few TEs from the history of science, I show that the replacement (...) thesis about TE is a failure. The paper is divided into three sections. The first section discusses the arguments of Chandrasekharan et al. (2013) and demonstrates the three distinct aspects of the replacement thesis. The second section examines the argument against TE and shows that they are inadequate to prove the withering of TE from science. The third section discusses Albert Einstein’s Magnet and Conductor TE and demonstrates that replacing such TE with CS yield no advantage. (shrink)

We propose a new way of looking at the quantum Maxwell’s demon problem in terms of conditional action. A “conditional action” on a system is a unitary time evolution, selected according to the result of a previous measurement, which can reduce the entropy of the system. However, any conditional action can be realized by an unitary time evolution of a larger system and a subsequent Lüders measurement, whereby the entropy of the entire system is either increased or remains constant. We (...) give some examples that illustrate and confirm our proposal, including the erasure of N qubits and the Szilard engine, thus relating the present approach to the Szilard principle and the Landauer principle that have been discussed as possible solutions of the Maxwell’s demon problem. (shrink)

This article distinguishes two different senses of information-theoretic approaches to statistical mechanics that are often conflated in the literature: those relating to the thermodynamic cost of computational processes and those that offer an interpretation of statistical mechanics where the probabilities are treated as epistemic. This distinction is then investigated through Earman and Norton’s ([1999]) ‘sound’ and ‘profound’ dilemma for information-theoretic exorcisms of Maxwell’s demon. It is argued that Earman and Norton fail to countenance a ‘sound’ information-theoretic interpretation and this paper (...) describes how the latter inferential interpretations can escape the criticisms of Earman and Norton ([1999]) and Norton ([2005]) by adopting this ‘sound’ horn. This article considers a standard model of Maxwell’s demon to illustrate how one might adopt an information-theoretic approach to statistical mechanics without a reliance on Landauer’s principle, where the incompressibility of the probability distribution due to Liouville’s theorem is taken as the central feature of such an interpretation. (shrink)

When considering controversial thermodynamic scenarios such as Maxwell's demon, it is often necessary to consider probabilistic mixtures of states. This raises the question of how, if at all, to assign entropy to them. The information-theoretic entropy is often used in such cases; however, no general proof of the soundness of doing so has been given, and indeed some arguments against doing so have been presented. We offer a general proof of the applicability of the information-theoretic entropy to probabilistic mixtures of (...) macrostates, making clear the assumptions on which it depends, in particular a probabilistic version of the Kelvin statement of the Second Law. We briefly discuss the interpretation of our result. (shrink)

Ladyman, Presnell, and Short proposed a model of the implementation of logical operations by physical processes in order to clarify the exact statement of Landauer's Principle, and then offered a new proof of the latter based on the construction of a thermodynamic cycle, arguing that if Landauer's Principle were false it would be possible to harness a machine that violated it to produce a violation of the second law of thermodynamics. In a recent paper in this journal, John Norton directly (...) challenges the consistency of that proof. In the present paper we defend the proof given by Ladyman et al. against his critique. In particular, contrary to what Norton claims, we argue that the processes used in the proof cannot be used to construct a cycle that enacts erasure in a thermodynamically reversible way, and that he does not show that the processes used in the proof violate the Second Law of Thermodynamics. (shrink)

Even though the second law of thermodynamics holds the supreme position among the laws of nature, as stated by many distinguished scientists, notably Eddington and Einstein, its position appears to be also quite peculiar. Given the atomic nature of matter, whose behavior is well described by statistical physics, the second law could not hold unconditionally, but only statistically. It is not an absolute law. As a result of this, in the present paper we try to argue that we have not (...) yet any truly cogent argument to exclude its possible macroscopic violation. Even Landauer's information-theoretic principle seems to fall short of the initial expectations of being the fundamental ‘physical’ reason of all Maxwell's demons failure. Here we propose a modified Szilard engine which operates without any steps in the process resembling the creation or destruction of information. We argue that the information-based exorcisms must be wrong, or at the very least superfluous, and that the real physical reason why such engines cannot work lies in the ubiquity of thermal fluctuations.We see in the above peculiar features the main motivation and rationale for pursuing exploratory research to challenge the second law, which is still ongoing and probably richer than ever. A quite thorough description of some of these challenges is also given. (shrink)

Recently Albert and Hemmo and Shenker have argued that, contrary to what is sometimes suggested, Liouville's theorem does not prohibit a Maxwellian demon from operating but merely places certain restrictions on its ability to operate. There are two main claims made in this article. First, that the restrictions Liouville's theorem places on Maxwell's demon's ability to operate depend on which notion of entropy one adopts. Second, that when one operates with the definition of entropy that is usual in this debate, (...) the restrictions put on Maxwell's demon are not even as severe as Albert and Hemmo and Shenker argue. (shrink)