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InTech eBooks

Quantum Dynamics, Entropy and Quantum Versions of Maxwell’s Demon

Paul Bracken

Published Aug 24, 2016• 3 citations
Publisher

Abstract

Several subjects which reside in the overlap area of quantum mechanics, statistical physics and thermodynamics are investigated in depth. This collection of subjects shares a common domain which is referred to as Maxwell’s demon. The classical version of this idea is introduced, and then, the contribution made by Szilard to the subject is presented. Several demons are considered, and it is shown that to best understand this area, quantum mechanics and the role information plays in it must be appreciated deeply.

DOI
10.5772/63563

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Several subjects which reside in the overlap area of quantum mechanics, statistical physics and thermodynamics are investigated in depth. This collection of subjects shares a common domain which is referred to as Maxwell’s demon. The classical version of this idea is introduced, and then, the contribution made by Szilard to the subject is presented. Several demons are considered, and it is shown that to best understand this area, quantum mechanics and the role information plays in it must be appreciated deeply.
Maxwell’s demon emanates from a thought experiment proposed by James Clerk Maxwell in 1867 to illustrate the statistical nature of the second law of thermodynamics. Subsequently researchers wondered whether such a demon could in fact violate the second law. Leon Brillouin argued that the entropy produced during the demon’s measurement precluded such a violation. Years later Oliver Penrose and Charles Bennett observed (independently) that a Maxwell’s demon gathers information and stores it in a memory. Penrose showed that erasure of such a memory sends sufficient entropy to the environment to preclude violation of the second law. Notably this is so even when measurement produces arbitrarily little entropy. Bennett obtained the same result using Rolf Landauer’s seminal research on the thermodynamics of computation. The stunning shift in focus from measurement to erasure provided the impetus to better understand the role of information in quantum mechanics and thermodynamics. Indeed the linkage of information with physics is the principal legacy of Maxwell’s demon. Szilard’s one‐particle classical “gas” model and its quantum mechanical extension, together with postulated connections between entropy and algorithmic information, have provided useful insights. We review the long history of Maxwell’s demon and assess the current status of the second law in the context of the demon’s operations.
Maxwell's demon was born in 1867 and still thrives in modern physics. He plays important roles in clarifying the connections between two theories: thermodynamics and information. Here the history of the demon and a variety of interesting consequences of the second law of thermodynamics are presented, mainly in quantum mechanics, but also in the theory of gravity. Also highlighted are some of the recent work that explores the role of information, illuminated by Maxwell's demon, in the arena of quantum-information theory.
A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. This paper proposes experimentally realizable models of quantum Maxwell's demons, explicates their thermodynamics, and shows how the information produced by quantum measurement and by decoherence acts as a source of thermodynamic inefficiency.
This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of “Maxwell’s Demon”, a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell’s challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The more recent proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through a neglected feature of quantum theory, namely the Heisenberg Uncertainty Principle, which also decisively serves to defeat the Demon.
Demon, the famous thought experiment of James Clerk Maxwell, has been devised in 1867 as a counter example for the Second Law of thermodynamics. During the 140 years since the Demon was first suggested, numerous attempts have been made to counter Maxwell's argument. The attempts have been to show that Maxwell was wrong, since his Demon cannot work for one reason or another (see Leff and Rex 2003 for details and references). In this paper we show (following an argument by Albert 2000, Ch. 5.) that Maxwell was basically right, in the sense that his thought experiment is compatible with the laws of mechanics as well as with central principles of statistical mechanics. We then derive some (weak) restrictions on the Demon's efficiency. Finally, we prove that the Demon's cycle of operation can be completed (in particular, the Demon's memory can be erased) without increasing the total entropy of the universe. We draw some conclusions about the way to understand the meaning and role of probability in classical statistical mechanics
This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of ``Maxwell's Demon'', a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell's challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through neglected features of quantum theory. In particular, an application of the Heisenberg Uncertainty Principle is shown to decisively defeat the Demon, as well as to serve as justification for Landauer's Principle, albeit in terms distinct from the usual computational formulation.