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)

In this second part of our two-part paper we review and analyse attempts since 1950 to use information theoretic notions to exorcise Maxwell’s Demon. We argue through a simple dilemma that these attempted exorcisms are ineffective, whether they follow Szilard in seeking a compensating entropy cost in information acquisition or Landauer in seeking that cost in memory erasure. In so far as the Demon is a thermodynamic system already governed by the Second Law, no further supposition about information and entropy (...) is needed to save the Second Law. In so far as the Demon fails to be such a system, no supposition about the entropy cost of information acquisition and processing can save the Second Law from the Demon. (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)

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.

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)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can happen can (...) just as naturally happen backwards. Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem. The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students. Table of Contents: Preface 1. Time-Reversal Invariance 2. Thermodynamics 3. Statistical Mechanics 4. The Reversibility Objections and the Past-Hypothesis 5. The Scope of Thermodynamics 6. The Asymmetries of Knowledge and Intervention 7. Quantum Mechanics Appendix: Gedankenexperiments with Heat Engines Index Reviews of this book: The foundations of statistical mechanisms are often presented in physics textbooks in a rather obscure and confused way. By challenging common ways of thinking about this subject, Time and Chance can do quite a lot to improve this situation. --Jean Bricmont, Science Albert is perfecting a style of foundational analysis that is uniquely his own...It has a surgical precision...and it is ruthless with pretensions. The foundations of thermodynamics is a topic that has accumulated a good deal of dead wood; this is a fire that will burn and burn. --Simon W. Saunders, Oxford University As usual with Albert's work, the exposition is brisk and to the point, and exceptionally clear...The book will be an extremely valuable contribution to the literature on the subject of philosophical issues in thermodynamics and statistical mechanics, a literature which has been thin on the ground but is now growing as it deserves to. --Lawrence Sklar, University of Michigan. (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)

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)

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)

Standard descriptions of thermodynamically reversible processes attribute contradictory properties to them: they are in equilibrium yet still change their state. Or they are comprised of non-equilibrium states that are so close to equilibrium that the difference does not matter. One cannot have states that both change and no not change at the same time. In place of this internally contradictory characterization, the term “thermodynamically reversible process” is here construed as a label for a set of real processes of change involving (...) only non-equilibrium states. The properties usually attributed to a thermodynamically reversible process are recovered as the limiting properties of this set. No single process, that is, no system undergoing change, equilibrium or otherwise, carries those limiting properties. The paper concludes with an historical survey of characterizations of thermodynamically reversible processes and a critical analysis of their shortcomings. (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)

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)

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 and Owen Maroney 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. 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)