This is an extensive review of recent work on the foundations of statistical mechanics.

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)

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)

In 1932, John von Neumann argued for the equivalence of the thermodynamic entropy and −Trρlnρ, since known as the von Neumann entropy. Meir Hemmo and Orly R. Shenker recently challenged this argument by pointing out an alleged discrepancy between the two entropies in the single-particle case, concluding that they must be distinct. In this article, their argument is shown to be problematic as it allows for a violation of the second law of thermodynamics and is based on an incorrect calculation (...) of the von Neumann entropy. (shrink)

In this paper recent work that attempts to link quantum entanglement to (i) thermodynamic energy, (ii) thermodynamic entropy and (iii) information is reviewed. With respect to the first two links the paper is essentially expository. The final link is elaborated on: it is argued that the value of the entanglement of a bipartite system in a pure state is equal to the value of the irreducible uncertainty (i.e. irreducibly missing information) about its subsystems and that this suggests that entanglement gives (...) rise to irreducible uncertainty. (The exact meaning of the phrase “irreducible uncertainty”, as used here, is explained in the body of the paper. Roughly speaking, it is the uncertainty about the post-measurement state of a system that cannot be removed at the pre-measurement stage.) This analysis is used to make a further connection between entanglement and statistical mechanical entropy: it is argued that these properties are indirectly linked, in so far as both give rise to forms of uncertainty (albeit rather different forms of uncertainty about rather different things). (shrink)

One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous departure from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the (...) formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions—monstrous Schr¨odinger cats—and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. (shrink)

Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather than (...) on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert’s time-dependent projection operator formalism. This allows to better understand how general proposals for understanding probability in statistical mechanics, namely quantum approaches and almost-objective probabilities, can be accomodated in the MZ formalism. Moreover, I will provide a detailed physical analysis, based on the MZ formalism, of various proposals from the philosophical literature, such as Robertson’s theory of justifying coarse-graining via autonomous macrodynamics, Myrvold’s problem of explaining autonomous macrodynamics, and Wallace’s simple dynamical conjecture. (shrink)