Kiessling, Michael K.-H. (2019) The influence of gravity on the Boltzmann entropy of a closed universe. [Preprint]

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Text (Invited, refereed contribution to the volume ``Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism, and the Laws of Nature,'' edited by Valia Allori.) KieALLORIvolumeREV.pdf - Accepted Version Download (459kB) | Preview

Abstract

This contribution inquires into Clausius' proposal that ``the entropy of the world tends to a maximum.'' The question is raised whether the entropy of `the world' actually does have a maximum; and if the answer is ``Yes!,''
what such states of maximum entropy look like, and if the answer is ``No!,'' what this could entail for the fate of the universe. Following R. Penrose, `the world' is modelled by a closed Friedman--Lema\^{\i}tre type universe, in which a three-dimensional spherical `space' is filled with `matter' consisting of $N$ point particles, their large-scale distribution being influenced by their own gravity.
As `entropy of matter' the Boltzmann entropy for a (semi-) classical macrostate, and Boltzmann's ergodic ensemble formulation of it for an isolated thermal equilibrium state, are studied. Since the notion of a Boltzmann entropy is not restricted to classical non-relativistic physics, the inquiry will take into account quantum theory as well as relativity theory; we also consider black hole entropy. Model universes having a maximum entropy state and those which don't will be encountered. It is found that the answer to our maximum entropy question is not at all straightforward at the general-relativistic level. In particular, it is shown that the increase in Bekenstein--Hawking entropy of general-relativistic black holes does
not always compensate for the Boltzmann entropy of a piece of matter swallowed by a black hole.

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Item Type:	Preprint
Creators:	Creators Email ORCID Kiessling, Michael K.-H. miki@math.rutgers.edu 0000-0001-8582-9560
Keywords:	Entropy; Gravity; Closed universe
Subjects:	Specific Sciences > Physics > Cosmology General Issues > Laws of Nature Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User:	Dr/ Michael K.-H. Kiessling
Date Deposited:	16 May 2019 13:58
Last Modified:	16 May 2019 13:58
Item ID:	16002
Subjects:	Specific Sciences > Physics > Cosmology General Issues > Laws of Nature Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date:	10 May 2019
URI:	https://philsci-archive.pitt.edu/id/eprint/16002

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