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Cambridge University Press eBooks

Maxwell’s Demon Does not Compute

John D. Norton

Published May 17, 2018• 5 citations
Publisher

Abstract

Must a Maxwell demon must fail to reverse the second law of thermodynamics? Standard attempts to show it must fail make use of notions of information and computation. None of these attempts have succeeded. Worse they have distracted both supporters and opponents of these attempts from a much simpler demonstration of the necessary failure of a Maxwell's demon that employs no notions of information or computation. It requires only Liouville's theorem and its quantum analog.

DOI
10.1017/9781316759745.012

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Must a Maxwell demon must fail to reverse the second law of thermodynamics? Standard attempts to show it must fail make use of notions of information and computation. None of these attempts have succeeded. Worse they have distracted both supporters and opponents of these attempts from a much simpler demonstration of the necessary failure of a Maxwell's demon that employs no notions of information or computation. It requires only Liouville's theorem and its quantum analog.
It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.
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.
Recently Albert and Hemmo and Shenker have argued that, contrary to what is sometimes suggested, Liouville's theorem does not prohibit a Maxwellian demon from operating but merely places certain restrictions on its ability to operate. There are two main claims made in this article. First, that the restrictions Liouville's theorem places on Maxwell's demon's ability to operate depend on which notion of entropy one adopts. Second, that when one operates with the definition of entropy that is usual in this debate, the restrictions put on Maxwell's demon are not even as severe as Albert and Hemmo and Shenker argue.
© 2016 Taylor & Francis It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.
Information thermodynamics is a generalization of thermodynamics to quantum systems and includes information as an analogy of negative entropy. This leads to a generalization of the second law in which the presence of quantum information is taken into account. Whether this information corresponds to conscious information, is left open. In an article published by Minagawa et al in Nature, a more rigorous proof than before is represented for the statement that the second law of thermodynamics is also valid in quantum theory with information included. The presence of information makes possible an apparent local violation of the second law in the sense that the system can do more work than the Carnot law allows. However, Maxwell's demon requires metabolic energy to function and it loses it when demonizing. This energy must be compensated and the conclusion is that the second law of thermodynamics is valid.
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.