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

Text (Invited, refereed contribution to the volume ``Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism, and the Laws of Nature,'' edited by Valia Allori.)
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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 FriedmanLema\^{\i}tre type universe, in which a threedimensional spherical `space' is filled with `matter' consisting of $N$ point particles, their largescale 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 nonrelativistic 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 generalrelativistic level. In particular, it is shown that the increase in BekensteinHawking entropy of generalrelativistic 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  

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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:  http://philsciarchive.pitt.edu/id/eprint/16002 
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