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Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics
Open accessAbstract
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics. We adopt a new point of view which has emerged progressively in recent years, and which takes seriously into account the chaotic character of the microscopic time evolution. The emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of Boltzmann. The nonequilibrium steady states, in presence of a Gaussian thermostat, are described by SRB measures. In terms of these one can prove the Gallavotti–Cohen fluctuation theorem. One can also prove a general linear response formula and study its consequences, which are not restricted to near-equilibrium situations. At equilibrium one recovers in particular the Onsager reciprocity relations. Under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of Dettmann and Morriss. The results just mentioned hold so far only for classical systems; they do not involve large size, i.e., they hold without a thermodynamic limit.
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“Surprisingly, there are frequently some unexpected deep connections between these different entropies which are very interesting [24, 25, 26].”
From On the (Boltzmann) entropy of non-equilibrium systems (2004) · cites this paper as [26]
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Cites
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Self-citation
Research works printed but not linked: 27
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Cited by
Maes, C., & Netočný, K. (2003) · Journal of Statistical Physics · doi:10.1023/a:1021026930129 · Cited by 308
On the (Boltzmann) entropy of non-equilibrium systems
Goldstein, S., & Lebowitz, J. L. (2004) · Physica D: Nonlinear Phenomena · doi:10.1016/j.physd.2004.01.008 · Cited by 240
“= S(E ′, N, V ; u)− 3 2 Nk log(kT ′), (32) where T ′ = 23k (KE′/N) is the temperature corresponding to the energy E ′ and the right hand side is the configurational part of the equilibrium entropy of system (30) at energy E′.”
Background
Metadata
- Authors
- Ruelle, D.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Corresponding author
- Ruelle, David
- Venue
- Journal of Statistical Physics
- Published
- 1999-04
- Volume
- 95
- Issue
- 1-2
- Pages
- 393-468
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W1646534854
- Cited by
- 438
- References
- 65
- Citations by year
- 2026: 9 · 2025: 10 · 2024: 11 · 2023: 14 · 2022: 12 · 2021: 25 · 2020: 9 · 2019: 13 · 2018: 15 · 2017: 12 · 2016: 9 · 2015: 14 · 2014: 21 · 2013: 21 · 2012: 14
- FWCI
- 11.87
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springernature.com/gp/researchers/text-and-data-mining (tdm)
- www.springernature.com/gp/researchers/text-and-data-mining (vor)
- Locations
- Journal of Statistical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- nonequilibrium statistical mechanics, nonequilibrium steady states, smooth dynamical systems, SRB measures, Gaussian thermostat, Gallavotti-Cohen fluctuation theorem, linear response, Onsager reciprocal relations
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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