dorsal/arxiv
View SchemaExplanation of the Gibbs paradox within the framework of quantum thermodynamics
| Authors | A. E. Allahverdyan, Th. M. Nieuwenhuizen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507145 |
| URL | https://arxiv.org/abs/quant-ph/0507145 |
| DOI | 10.1103/PhysRevE.73.066119 |
| Journal | Phys. Rev. E 73, 066119 (2006) [15 pages] |
Abstract
The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally looses its dominant place and the target of the paradox is naturally shifted to the decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of ``difference between the gases'' gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counter-intuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases, or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.
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"abstract": "The issue of the Gibbs paradox is that when considering mixing of two gases\nwithin classical thermodynamics, the entropy of mixing appears to be a\ndiscontinuous function of the difference between the gases: it is finite for\nwhatever small difference, but vanishes for identical gases. The resolution\noffered in the literature, with help of quantum mixing entropy, was later shown\nto be unsatisfactory precisely where it sought to resolve the paradox.\nMacroscopic thermodynamics, classical or quantum, is unsuitable for explaining\nthe paradox, since it does not deal explicitly with the difference between the\ngases. The proper approach employs quantum thermodynamics, which deals with\nfinite quantum systems coupled to a large bath and a macroscopic work source.\nWithin quantum thermodynamics, entropy generally looses its dominant place and\nthe target of the paradox is naturally shifted to the decrease of the maximally\navailable work before and after mixing (mixing ergotropy). In contrast to\nentropy this is an unambiguous quantity. For almost identical gases the mixing\nergotropy continuously goes to zero, thus resolving the paradox. In this\napproach the concept of ``difference between the gases\u0027\u0027 gets a clear\noperational meaning related to the possibilities of controlling the involved\nquantum states. Difficulties which prevent resolutions of the paradox in its\nentropic formulation do not arise here. The mixing ergotropy has several\ncounter-intuitive features. It can increase when less precise operations are\nallowed. In the quantum situation (in contrast to the classical one) the mixing\nergotropy can also increase when decreasing the degree of mixing between the\ngases, or when decreasing their distinguishability. These points go against a\ndirect association of physical irreversibility with lack of information.",
"arxiv_id": "quant-ph/0507145",
"authors": [
"A. E. Allahverdyan",
"Th. M. Nieuwenhuizen"
],
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"quant-ph",
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],
"doi": "10.1103/PhysRevE.73.066119",
"journal_ref": "Phys. Rev. E 73, 066119 (2006) [15 pages]",
"title": "Explanation of the Gibbs paradox within the framework of quantum thermodynamics",
"url": "https://arxiv.org/abs/quant-ph/0507145"
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