Werndl, Charlotte and Frigg, Roman (2024) The Boltzmann Equation and Its Place in the Edifice of Statistical Mechanics. Entropy.
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Abstract
It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and BSM, we first present a version of BSM that differs from standard presentation in that it uses local field variables
to individuate macro-states, and we then show that BE is a special case of BSM thus understood. To discuss the relation between BE and GSM, we focus on the BBGKY hierarchy and note the version of the BE that follows from the hierarchy is “Gibbsian” only in the minimal sense that it operates with
an invariant measure on the state space of the full system.
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| Item Type: | Published Article or Volume | |||||||||
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| Additional Information: | Research from Charlotte Werndl was funded in whole or in part by the Austrian Science Fund (FWF) [grant DOI: 10.55776/CO3]. For open access purposes, the author has applied a CC BY public copyright license to any author accepted manuscript version arising from this submission. | |||||||||
| Keywords: | Boltzmann equation; Boltzmann; Gibbs; statistical mechanics; macro-states; BBGKY hierarchy | |||||||||
| Subjects: | Specific Sciences > Physics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Statistical Mechanics/Thermodynamics |
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| Depositing User: | Charlotte Werndl | |||||||||
| Date Deposited: | 12 Jun 2025 12:31 | |||||||||
| Last Modified: | 12 Jun 2025 12:31 | |||||||||
| Item ID: | 25679 | |||||||||
| Journal or Publication Title: | Entropy | |||||||||
| Official URL: | https://www.mdpi.com/1099-4300/26/12/1106 | |||||||||
| Subjects: | Specific Sciences > Physics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Statistical Mechanics/Thermodynamics |
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| Date: | December 2024 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/25679 |
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