Boltzmann’s Approach to Statistical Mechanics
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
Boltzmann defined the entropy of a macroscopic system with microstate X as the logarithm of the phase-space volume corresponding to its macrostate M.
“Boltzmann defined the entropy of a macroscopic system with microstate X by”
From On the (Boltzmann) entropy of non-equilibrium systems (2004) · cites this paper as [9]
Cites
The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics
Penrose, R., & Gardner, M. (1989) · doi:10.1093/oso/9780198519737.001.0001 · Cited by 2,007 · see citing works
Boltzmann's Entropy and Time's Arrow
Lebowitz, J. L. (1993) · Physics Today · doi:10.1063/1.881363 · Cited by 571 · see citing works
What is Life?: With Mind and Matter and Autobiographical Sketches
Schrödinger, E., & Penrose, R. (1992) · doi:10.1017/cbo9781139644129 · Cited by 568 · see citing works
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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 · see citing works
Self-citationGoverning Without A Fundamental Direction of Time: Minimal Primitivism about Laws of Nature
Chen, E. K., & Goldstein, S. (2022) · Jerusalem Studies in Philosophy and History of Science · doi:10.1007/978-3-030-96775-8_2 · Cited by 69 · see citing works
“(1992) and Goldstein (2017).) In fact, it is also possible to interpret stochastic dynamics as yielding a typicality measure: the GRW theory specifies a probability distribution over entire histories of the quantum states, and what matters is the behavior of “almost all” of those possible histories.”
BackgroundResultSelf-citationThe Past Hypothesis and the Nature of Physical Laws
Chen, E. K. (2020) · arXiv · doi:10.48550/arxiv.2008.00611 · Cited by 14 · see citing works
- Authors
- Goldstein, S.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Corresponding author
- Goldstein, Sheldon
- Venue
- Lecture Notes in Physics
- Publisher
- Springer Berlin Heidelberg
- Published
- 2001
- Pages
- 39-54
- ISSN
- 0075-8450 (ISSN-L)
- OpenAlex
- W1680443341
- Cited by
- 213
- References
- 3
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 7 · 2023: 31 · 2022: 10 · 2021: 9 · 2020: 16 · 2019: 7 · 2018: 4 · 2017: 11 · 2016: 3 · 2015: 10 · 2014: 6 · 2013: 10 · 2012: 4
- FWCI
- 8.80
- Type
- book chapter
- Language
- en
- Open access
- closed
- 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
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy and History of Science
- Keywords
- Ludwig Boltzmann, statistical mechanics, second law of thermodynamics, irreversibility, H-theorem, Gibbs entropy, phase space probability distribution, thermodynamic entropy, ergodicity, mixing, foundations of statistical mechanics
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.
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