In:
Journal of Applied Probability, Cambridge University Press (CUP), Vol. 43, No. 04 ( 2006-12), p. 1028-1043
Abstract:
In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems.
Type of Medium:
Online Resource
ISSN:
0021-9002
,
1475-6072
DOI:
10.1017/S0021900200002400
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2006
detail.hit.zdb_id:
1474599-9
detail.hit.zdb_id:
219147-7
SSG:
3,2
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