Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie
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I. Ci7ePber cerschiedene j'iir die .dnwendung bequeineFormen der Hauptgleichuiigen der mechanischen Wiirinetheorie; con R
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For N noninteracting point particles moving among a periodic array of scatterers, starting from a nonuniform initial density f_X0, the time-evolved f_Xt approaches a distribution depending only on |v| and having larger S_gas(f).
“Starting with a nonuniform initial density f X 0 ( x , v ) the time evolved f X t ( x , v ) will approach an f which depends only on | v | and which will have a larger S gas ( f ).”
From On the (Boltzmann) entropy of non-equilibrium systems (2004) · cites this paper as [10]
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 [10]
When the periodicity of the scatterers is on the microscopic scale, then for macroscopic times the spatial density profile n_Xt(x) satisfies a diffusion equation.
“We note that when the periodicity of the scatterers is on the microscopic scale then for macroscopic times the spatial density profile n X t ( x ) will satisfy a diffusion equation [7, 10].”
From On the (Boltzmann) entropy of non-equilibrium systems (2004) · cites this paper as [10]
Cited by
Sorted by citations
Wehrl, A. (1978) · Reviews of Modern Physics · doi:10.1103/revmodphys.50.221 · Cited by 1,963 · see citing works
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
The Development of Boltzmann’s Statistical Ideas
Klein, M. J. (1973) · The Boltzmann Equation · doi:10.1007/978-3-7091-8336-6_4 · Cited by 74 · see citing works
- Authors
- Clausius, R.
- Corresponding author
- Clausius, R.
- Venue
- Annalen der Physik
- Publisher
- Wiley
- Published
- 1865-01
- Volume
- 201
- Issue
- 7
- Pages
- 353-400
- ISSN
- 0003-3804 (ISSN-L)
- 1521-3889
- OpenAlex
- W2074412592
- Cited by
- 507
- References
- 0
- Citations by year
- 2026: 28 · 2025: 34 · 2024: 26 · 2023: 28 · 2022: 41 · 2021: 26 · 2020: 21 · 2019: 22 · 2018: 16 · 2017: 22 · 2016: 19 · 2015: 18 · 2014: 13 · 2013: 12 · 2012: 18
- FWCI
- 74.50
- Type
- journal article
- Language
- en
- Open access
- green
- zenodo.org
- Licence
- Locations
- Annalen der Physik (publishedVersion)
- Zenodo (CERN European Organization for Nuclear Research) (submittedVersion, public-domain)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Engineering › Computational Mechanics › Heat Transfer and Numerical Methods
- Physical Sciences › Engineering › Mechanics of Materials › Thermoelastic and Magnetoelastic Phenomena
- Keywords
- mechanical theory of heat, thermodynamic equations, thermodynamic potential, equation of state, thermodynamics
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