Von Neumann argued by means of a thought experiment involving measurements of spin observables that the quantum mechanical quantity is conceptually equivalent to thermodynamic entropy. We analyze Von Neumann's thought experiment and show that his argument fails. Over the past few years there has been a dispute in the literature regarding the Von Neumann entropy. It turns out that each contribution to this dispute addressed a different special case. In this paper we generalize the discussion and examine the full matrix (...) of possibilities that are relevant for the evaluation and understanding of Von Neumann’s argument. (shrink)

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)

The main aim of this work is to contribute tothe elucidation of the concept of informationby comparing three different views about thismatter: the view of Fred Dretske's semantictheory of information, the perspective adoptedby Peter Kosso in his interaction-informationaccount of scientific observation, and thesyntactic approach of Thomas Cover and JoyThomas. We will see that these views involvevery different concepts of information, eachone useful in its own field of application. This comparison will allow us to argue in favorof a terminological `cleansing': it (...) is necessaryto make a terminological distinction among thedifferent concepts of information, in order toavoid conceptual confusions when the word`information' is used to elucidate relatedconcepts as knowledge, observation orentropy. (shrink)

In the present paper we develop different arguments to show that there are no reasons to consider that there exists quantum information as qualitatively different than Shannon information. There is only one kind of information, which can be coded by means of orthogonal or non-orthogonal states. The analogy between Shannon’s theory and Schumacher’s theory is confined to coding theorems. The attempt to extend the analogy beyond this original scope leads to a concept of quantum information that becomes indistinguishable from that (...) of quantum state. But information is essentially linked with communication, as it is clear in both Shannon’s and Schumacher’s proposals. If we detach information from this link, we are not talking about information but about quantum mechanics. We also stress the neutrality of information with respect to the physical theories that describe the systems used for its implementation. This view opens the way towards a non-reductive unification of physics: if different physical theories can be reconstructed on the same neutral informational basis, they could be meaningfully compared with no need of searching for reductive links among them. (shrink)

Christopher Timpson proposes a deflationary view about information, according to which the term ‘information’ is an abstract noun and, as a consequence, information is not part of the material contents of the world. The main purpose of the present article consists in supplying a critical analysis of this proposal, which will lead us to conclude that information is an item even more abstract than what Timpson claims. From this view, we embrace a pluralist stance that recognizes the legitimacy of different (...) interpretations of the concept of information. (shrink)

It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as 'ignorance' probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role (...) of probability in explanation and laws. This is the 'paradox of deterministic probabilities'. After surveying the usual list of accounts of objective chance and finding them inadequate I argue that an account of chance sketched by David Lewis can be modified to solve the paradox of deterministic probabilities and provide an adequate account of the probabilities in deterministic theories like statistical mechanics. (shrink)

This book argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, this book demonstrates how to build a metaphysics compatible with current fundamental physics, which, when combined (...) with metaphysics of the special sciences, can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, this book argues, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. The text assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the books' metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism versus empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds. (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)

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)

In this paper we analyze the relation between the notion of typicality and the notion of probability and the related question of how the choice of measure in deterministic theories in physics may be justified. Recently it has been argued that although the notion of typicality is not a probabilistic notion, it plays a crucial role in underwriting probabilistic statements in classical statistical mechanics and in Bohm’s theory. We argue that even in theories with deterministic dynamics, like classical statistical mechanics (...) and Bohm’s theory, the notion of probability can be understood as fundamentally objective, and that it is the notion of probability rather than typicality that may have an explanatory value. (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)

This paper proves that Maxwell's Demon is compatible with classical mechanics. In particular it shows how the cycle of operation - including measurement and erasure - can be carried out with no entropy cost, contrary to the Landauer-Bennett thesis (according to which memory erasure costs kln2 of entropy increase per bit). The Landauer-Bennet thesis is thus proven to be mistaken.

An important contemporary version of Boltzmannian statistical mechanics explains the approach to equilibrium in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognized as such and not clearly distinguished. This article identifies three different versions of typicality‐based explanations of thermodynamic‐like behavior and evaluates their respective successes. The conclusion is that the first two are unsuccessful because they fail to take the system's dynamics into account. The third, however, is promising. (...) I give a precise formulation of the proposal and present an argument in support of its central contention. †To contact the author, please write to: Department of Philosophy, Logic, and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, England; e‐mail: [email protected]. (shrink)

Focusing on Shannon information, this article shows that, even on the basis of the same formalism, there may be different interpretations of the concept of information, and that disagreements may be deep enough to lead to very different conclusions about the informational characterization of certain physical situations. On this basis, a pluralist view is argued for, according to which the concept of information is primarily a formal concept that can adopt different interpretations that are not mutually exclusive, but each useful (...) in a different specific context. (shrink)

Luciano Floridi presents a book that will set the agenda for the philosophy of information. PI is the philosophical field concerned with the critical investigation of the conceptual nature and basic principles of information, including its dynamics, utilisation, and sciences, and the elaboration and application of information-theoretic and computational methodologies to philosophical problems. This book lays down, for the first time, the conceptual foundations for this new area of research. It does so systematically, by pursuing three goals. Its metatheoretical goal (...) is to describe what the philosophy of information is, its problems, approaches, and methods. Its introductory goal is to help the reader to gain a better grasp of the complex and multifarious nature of the various concepts and phenomena related to information. Its analytic goal is to answer several key theoretical questions of great philosophical interest, arising from the investigation of semantic information. (shrink)

The law of gravitation, an example of physical law The relation of mathematics to physics The great conservation principles Symmetry in physical law The distinction of past and future Probability and uncertainty: the quantum mechanical view of nature Seeking new laws.

In this first part of a two-part paper, we describe efforts in the early decades of this century to restrict the extent of violations of the Second Law of thermodynamics that were brought to light by the rise of the kinetic theory and the identification of fluctuation phenomena. We show how these efforts mutated into Szilard’s proposal that Maxwell’s Demon is exorcised by proper attention to the entropy costs associated with the Demon’s memory and information acquisition. In the second part (...) we will argue that the information theoretic exorcisms of the Demon provide largely illusory benefits. According to the case, they either return a presupposition that can be had without information theoretic consideration or they postulate a broader connection between information and entropy than can be sustained. (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)

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

This article argues that most of the approaches to the foundations of statistical mechanics have severed their link with the original foundational project, the project of demonstrating how real mechanical systems can behave thermodynamically.

I recently reviewed Hemmo and Shenker's book "The Road to Maxwell's Demon" and the authors subsequently replied to my criticism. Here is my response to them.

Information theory and statistical mechanics II.

Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

This paper investigates what the source of time-asymmetry is in thermodynamics, and comments on the question whether a time-symmetric formulation of the Second Law is possible.

Landauer's principle, often regarded as the basic principle of the thermodynamics of information processing, holds that any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment. Conversely, it is generally accepted that any logically reversible transformation of information can in principle be accomplished by an appropriate physical mechanism operating in a (...) thermodynamically reversible fashion. These notions have sometimes been criticized either as being false, or as being trivial and obvious, and therefore unhelpful for purposes such as explaining why Maxwell's Demon cannot violate the second law of thermodynamics. Here I attempt to refute some of the arguments against Landauer's principle, while arguing that although in a sense it is indeed a straightforward consequence or restatement of the Second Law, it still has considerable pedagogic and explanatory power, especially in the context of other influential ideas in nineteenth and twentieth century physics. Similar arguments have been given by Jeffrey Bub. (shrink)

Book review of Meir Hemmo and Orly Shenker's book "The Road to Maxwell's Demon: Conceptual Foundations of Statistical Mechanics.".

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...) view of science as a construction of models to represent the phenomena. (shrink)

It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford’s theorem (...) succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all. (shrink)

The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-reversal (non-)invariance and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Caratheodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It (...) is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-reversal non-invariance plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. (shrink)

In quantum mechanics, the expression for entropy is usually taken to be -kTr(ln), where is the density matrix. The convention first appears in Von Neumann's Mathematical Foundations of Quantum Mechanics. The argument given there to justify this convention is the only one hitherto offered. All the arguments in the field refer to it at one point or another. Here this argument is shown to be invalid. Moreover, it is shown that, if entropy is -kTr(ln), then perpetual motion machines are possible. (...) This and other considerations support the conclusion that this expression is not the quantum-mechanical correlate of thermodynamic entropy. Its usefulness in quantum-statistical mechanics can be explained by its being a convenient quantification of information, but information and entropy are not synonymous. As the present paper shows, one can change while the other is conserved. (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)

The mathematical theory of communication.

This book helps us understand the true meaning of the concept and how it can be used to understand our world.

Every Thing Must Go aruges that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it ...

A classic source for understanding the connections between information theory and physics, this text was written by one of the giants of 20th-century physics and is appropriate for upper-level undergraduates and graduate students. Topics include the principles of coding, coding problems and solutions, the analysis of signals, a summary of thermodynamics, thermal agitation and Brownian motion, and thermal noise in an electric circuit. A discussion of the negentropy principle of information introduces the author's renowned examination of Maxwell's demon. Concluding chapters (...) explore the associations between information theory, the uncertainty principle, and physical limits of observation, in addition to problems related to computing, organizing information, and inevitable errors. 1962 ed. 81 figures. 14 tables. (shrink)

This book explores the role of causal constraints in science, shifting our attention from causal relations between individual events--the focus of most philosophical treatments of causation--to a broad family of concepts and principles generating constraints on possible change. Yemima Ben-Menahem looks at determinism, locality, stability, symmetry principles, conservation laws, and the principle of least action-causal constraints that serve to distinguish events and processes that our best scientific theories mandate or allow from those they rule out. Ben-Menahem's approach reveals that causation (...) is just as relevant to explaining why certain events fail to occur as it is to explaining events that do occur. She investigates the conceptual differences between, and interrelations of, members of the causal family, thereby clarifying problems at the heart of the philosophy of science. Ben-Menahem argues that the distinction between determinism and stability is pertinent to the philosophy of history and the foundations of statistical mechanics, and that the interplay of determinism and locality is crucial for understanding quantum mechanics. Providing historical perspective, she traces the causal constraints of contemporary science to traditional intuitions about causation, and demonstrates how the teleological appearance of some constraints is explained away in current scientific theories such as quantum mechanics. (shrink)