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On the Entropy of a One-Dimensional Gas with and without Mixing Using Sinai Billiard.

ABSTRACT: A one-dimensional gas comprising N point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann-Gibbs. Due to the collisions, trajectories of gas particles are strongly correlated and exhibit both chaotic and periodic properties. Probability distributions for the position of each particle in the one-dimensional gas can be obtained analytically, elucidating that the entropy in this special case is extensive at any given number N. Furthermore, the entropy obtained can be interpreted as a measure of the extent of interactions between molecules. The results obtained for the non-mixable one-dimensional system are generalized to mixable one- and two-dimensional systems, the latter by a simple example only providing similar findings.

SUBMITTER: Sobol A

PROVIDER: S-EPMC8467902 | biostudies-literature | 2021 Sep

REPOSITORIES: biostudies-literature

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On the Entropy of a One-Dimensional Gas with and without Mixing Using Sinai Billiard.

Sobol Alexander A Güntert Peter P Riek Roland R

Entropy (Basel, Switzerland) 20210909 9

A one-dimensional gas comprising <i>N</i> point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann-Gibbs. Due to the collisions, trajectories of gas particles are strongly correlated and exhibit both chaotic and periodic properties. Probability distributions for the position of each particle in the one-dimension ...[more]

PMID: 34573813

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