The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Time evolution of large classical systems
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Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“One starts with a nonequilibrium system with energy E in which the kinetic energy K is larger than what it would be for an equilibrium system with the same energy E . The system will evolve towards equilibrium with a Maxwellian velocity distribution at temperature T ∞ = 2 3 k K E where K E is the equilibrium kinetic energy corresponding to E .”
From On the (Boltzmann) entropy of non-equilibrium systems (2004) · cites this paper as [16]
In the citing paper
“However, since the microstates corresponding to the initial situation just described are not typical for the macrostates Γ f 0 , this example does not contradict the typical second law behavior of S ( f t ).”
From On the (Boltzmann) entropy of non-equilibrium systems (2004) · cites this paper as [16]
In the citing paper
“Assuming that f 0 is a Maxwellian with temperature T 0 we will have T ∞ < T 0 and so S gas ( f ∞ ) < S gas ( f 0 ).”
From On the (Boltzmann) entropy of non-equilibrium systems (2004) · cites this paper as [16]
Citations
Cites
Mathematical Methods in Kinetic Theory
Cercignani, C. (1990) · Springer eBooks · doi:10.1007/978-1-4899-7291-0 · Cited by 601
Mathematical Methods In Kinetic Theory
Cercignani, C., & Street, R. E. (1970) · Physics Today · doi:10.1063/1.3021788 · Cited by 373
Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
McKean, H. P. (1966) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00264463 · Cited by 286
On the Boltzmann equation for rigid spheres
Cercignani, C. (1972) · Transport Theory and Statistical Physics · doi:10.1080/00411457208232538 · Cited by 103
Cited by
Sorted by citations
Topics in propagation of chaos
Sznitman, A. (1991) · Lecture notes in mathematics · doi:10.1007/bfb0085169 · Cited by 1,358
A Review of Mathematical Topics in Collisional Kinetic Theory
Villani, C. (2002) · Handbook of mathematical fluid dynamics · doi:10.1016/s1874-5792(02)80004-0 · Cited by 842
Numerical methods for kinetic equations
Dimarco, G., & Pareschi, L. (2014) · Acta Numerica · doi:10.1017/s0962492914000063 · Cited by 358
The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels
Golse, F., & Saint‐Raymond, L. (2003) · Inventiones mathematicae · doi:10.1007/s00222-003-0316-5 · Cited by 290
Foundations of statistical mechanics
Penrose, O. (1979) · Reports on Progress in Physics · doi:10.1088/0034-4885/42/12/002 · Cited by 257
Metadata
- Authors
- Lanford, O. E.
- Affiliations
- University of California System (US)
- Corresponding author
- Lanford, Oscar E.
- Venue
- Lecture Notes in Physics
- Publisher
- Springer Berlin Heidelberg
- Published
- 1975
- Pages
- 1-111
- ISSN
- 0075-8450 (ISSN-L)
- 1616-6361
- OpenAlex
- W1568056205
- Cited by
- 557
- References
- 4
- Citations by year
- 2026: 7 · 2025: 18 · 2024: 19 · 2023: 17 · 2022: 22 · 2021: 14 · 2020: 17 · 2019: 16 · 2018: 21 · 2017: 14 · 2016: 22 · 2015: 22 · 2014: 35 · 2013: 15 · 2012: 20
- FWCI
- 32.95
- Type
- book chapter
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Lecture notes in physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Keywords
- nonequilibrium statistical mechanics, microcanonical ensemble, ergodic theory, time evolution, large-scale systems
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.
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