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Exact Solutions for Homogeneous Linear Biased Correlated Walks. A Case of the Boltzmann Entropy Decreasing in Time
Author(s) -
Godoy S. V.,
Fujita S.,
Rodriguez R.
Publication year - 1987
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221390104
Subject(s) - boltzmann constant , boltzmann equation , boltzmann's entropy formula , statistical physics , homogeneous , entropy (arrow of time) , mathematics , boundary value problem , constant (computer programming) , mathematical analysis , physics , thermodynamics , computer science , programming language
The probabilities of arrival with directions for a linear biased correlated walk satisfy a set of coupled linear difference equations. An exact analytic solution to the equations subject to a periodic‐boundary and homogeneous‐initial condition is obtained. The Boltzmann entropy (the negative of the Boltzmann constant k B times the Boltzmann H ‐function) computed in terms of the solution may decrease (or increase) in time, depending on the chosen initial condition. The physical meaning of this striking behavior is discussed by taking diatomic impurities (CO) in liquid solution (Ar) under external electric fields. It is concluded that in the presence of a bias the sense of the time‐development of a general physical system cannot be given by the conventional Boltzmann H ‐function.