Kinetic equations from Hamiltonian dynamics: Markovian limits
Abstract
Dynamical processes in macroscopic systems are often approximately described by kinetic and hydrodynamic equations. One of the central problems in nonequilibrium statistical mechanics is to understand the approximate validity of these equations starting from a microscopic model. We discuss a variety of classical as well as quantum-mechanical models for which kinetic equations can be derived rigorously. The probabilistic nature of the problem is emphasized: The approximation of the microscopic dynamics by either a kinetic or a hydrodynamic equation can be understood as the approximation of a non-Markovian stochastic process by a Markovian process.
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The local master equation is also obtained in the singular coupling limit, where the bath correlation functions tend to a delta function.
“We note that the local master equation is also obtained in the so-called singular coupling limit [1,5,10,12], where the bath correlation functions in equations (8) tend to a delta function.”
From Markovian master equations for quantum thermal machines: Local versus global approach (2017) · cites this paper as [10]
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- Authors
- Spohn, H.
- Affiliations
- Ludwig-Maximilians-Universität München (DE)
- Corresponding author
- Spohn, Herbert
- ORCID
- Spohn, Herbert
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1980-07-01
- Volume
- 52
- Issue
- 3
- Pages
- 569-615
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W2025185856
- Semantic Scholar
- 1d8721e598150bea8d3d2420b61e72c47ace4f6c
- Cited by
- 1,013
- References
- 126
- Citations by year
- 2026: 17 · 2025: 24 · 2024: 22 · 2023: 28 · 2022: 36 · 2021: 45 · 2020: 38 · 2019: 43 · 2018: 39 · 2017: 26 · 2016: 36 · 2015: 34 · 2014: 43 · 2013: 31 · 2012: 34
- FWCI
- 21.27
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Reviews of Modern Physics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- kinetic equations, Hamiltonian dynamics, Markov approximation, non-Markovian processes, hydrodynamic equations, nonequilibrium statistical mechanics, quantum kinetic theory, classical kinetic theory, stochastic processes
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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