Time evolution of large classical systems
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In Jaynes's example, a nonequilibrium system with energy E and kinetic energy K larger than equilibrium at the same E evolves toward equilibrium with a Maxwellian velocity distribution at temperature T∞ = (2/3k) K_E, where K_E is the equilibrium kinetic energy corresponding to E.
“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]
The Jaynes example does not contradict the typical second law behavior of S(f_t) because the microstates corresponding to the initial situation are not typical for the macrostates Γ_f0.
“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]
Assuming f0 is Maxwellian with temperature T0, then T∞ < T0 and S_gas(f∞) < S_gas(f0).
“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]
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- 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
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