Orly Shenker

We discuss a recent proposal by Albert to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wave function of Ghirardi, Rimini and Weber. 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, \eg Joos and Zeh and Zurek and Paz. This paper presents the two approaches and discusses their advantages. The problems they face will be discussed in a sequel.

Can we explain the laws of thermodynamics, in particular the irreversible increase of entropy, from the underlying quantum mechanical dynamics? Attempts based on classical dynamics have all failed. Albert (1994a,b; 2000) proposed a way to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wavefunction of Ghirardi, Rimini and Weber (1986). In this paper 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) and Zurek and Paz (1994).

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

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

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.

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.

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.

The appearance of multiple realization of the special sciences kinds by physical kinds can be fully explained within a type-identity reductive physicalist framework, based on recent findings in the foundations of statistical mechanics. This has been shown in Hemmo and Shenker. However, while this account is available for special sciences like biology and thermodynamics, it is unavailable for psychology. Therefore the only coherent physicalist account of psychology is a type-type identity account. The so-called “non reductive” physicalism turns out to be an incoherent idea, and functionalism and supervenience cannot salvage it. At the same time, within a type-identity account properly understood one can give a full account of the anomaly of psychology and understand in what sense the special sciences - including psychology - are autonomous.

The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are sub- sumed under the Second Law of Thermodynamics. This law characterizes our experience of the arrow of time in terms of an increase of a theoretical magnitude called entropy. Statistical mechan- ics tries to explain the Second Law as an effect of the behavior of the microscopic particles that make up the universe. Since our senses are too coarse to see this microstructure, statistical mechanics describes our experience in terms of probability, or in terms of the partial information we have about the particles. In this paper we explain the workings of statistical mechanics; how it accounts for probability as an objective feature of the world based on the underlying dynamics; how it accounts for our memories of the past; how the statistical mechanical probability under- writes the Second Law; and how, at the same time, it leads to a violation of the Second Law by the so-called Maxwell’s Demon.

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.

Mara Beller's book Quantum Dialogue: The Making of a Revolution is a book in history and historiography, which invites a philosophical reading. The book offers a new and quite radical approach in the philosophy of science, which Beller calls dialogism, and it demonstrates the application of this approach by studying cases in the history of physics. This paper reconstructs of some of the book's theses, in a way which emphasises its philosophical insights, and goes on to shows how philosophically far dialogism can take us. The example on which the paper focuses is the demarcation between science and non-science.

In recent years the magnificent world of fractals has been revealed. Some of the fractal images resemble natural forms so closely that Benoit Mandelbrot's hypothesis, that the fractal geometry is the geometry of natural objects, has been accepted by scientists and non-scientists alike. The present paper critically examines Mandelbrot's hypothesis. It first analyzes the concept of a fractal. The analysis reveals that fractals are endless geometrical processes, and not geometrical forms. A comparison between fractals and irrational numbers shows that the former are ontologically and epistemologically even more problematic than the latter. Therefore, it is argued, a proper understanding of the concept of fractal is inconsistent with ascribing a fractal structure to natural objects. Moreover, it is shown that, empirically, the so-called fractal images disconfirm Mandelbrot's hypothesis. It is conceded that the fractal geometry can be used as a useful rough approximation, but this fact has no bearing on the physical theory of natural forms

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).

Multiple realizability seems to be empirically justified and provides the conceptual basis for the autonomy of the special sciences. But it is mysterious. In this talk I propose a new reductionist approach to the special sciences that removes the mystery: I explain why the special sciences kinds appear to be multiply realized although they are identical with physical kinds and in what sense the special sciences kinds and laws are autonomous although they are physical laws. This approach is based on the approach by Hemmo & Shenker to the reduction of thermodynamics to statistical mechanics.

A remarkable thesis prevails in the physics of information, saying that the logical properties of operations that are carried out by computers determine their physical properties. More specifically, it says that logically irreversible operations are dissipative by klog2 per bit of lost information. (A function is logically irreversible if its input cannot be recovered from its output. An operation is dissipative if it turns useful forms of energy into useless ones, such as heat energy.) This is Landauer's dissipation thesis, hereafter LDT. LDT underlies and motivates numerous researches in physics and computer science. Nevertheless, this paper shows that is it plainly wrong. This conclusion is based on a detailed study of LDT in terms of the various notions of entropy used in main stream statistical mechanics. It is supported by a counter example for LDT. Further support is found in an analysis of the phase space representation on which LDT relies. This analysis emphasises the constraints placed on the choice of probability distribution by the fact that it has to be the basis for calculating phase averages corresponding to thermodynamic properties of individual systems. An alternative representation is offered, in which logical irreversibility has nothing to do with dissipation. The strong connection between logic and physics, that LDT implies, is thereby broken off.