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Reducing Thermodynamics to Boltzmannian Statistical Mechanics: The Case of Macro Values

Ehmann, Alexander (2022) Reducing Thermodynamics to Boltzmannian Statistical Mechanics: The Case of Macro Values. [Preprint]

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Abstract

Thermodynamic macro variables, such as the temperature or volume macro variable, can take on a continuum of allowable values, called thermodynamic macro values. Although referring to the same macro phenomena, the macro variables of Boltzmannian Statistical Mechanics (BSM) differ from thermodynamic macro variables in an important respect: within the framework of Boltzmannian Statistical Mechanics the evolution of macro values of systems with finite available phase space is invariably modelled as discontinuous, due to the method of partitioning phase space into macro regions with sharp, fixed boundaries. Conceptually, this is at odds with the continuous evolution of macro values as described by thermodynamics, as well as with the continuous evolution of the micro state assumed in BSM. This discrepancy I call the discontinuity problem (DP). I show how it arises from BSM’s framework and demonstrate its consequences, in particular for the foundational project of reducing thermodynamics to BSM: thermodynamic macro values are shown to not supervene on the corresponding BSM macro values. With supervenience being a conditio sine qua non for the kind of reduction envisaged by the foundational project, the latter is in jeopardy.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Ehmann, Alexanderalexanderehmann@alexanderehmann.com0000-0001-6735-0599
Additional Information: Forthcoming in Synthese
Keywords: Boltzmannian Statistical Mechanics; Phase Space Partitioning; Macro Region; Macro State; Macro Value; Reduction
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Dr. Alexander Ehmann
Date Deposited: 18 Nov 2022 17:15
Last Modified: 18 Nov 2022 17:15
Item ID: 21448
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: 16 November 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21448

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