caa a22 4500 467892113 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s10955-006-9099-6 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9099-6 A Simple Discrete Model of Brownian Motors: Time-periodic Markov Chains [Elektronische Daten] [Hao Ge, Da-Quan Jiang, Min Qian] In this paper, we consider periodically inhomogeneous Markov chains, which can be regarded as a simple version of physical model—Brownian motors. We introduce for them the concepts of periodical reversibility, detailed balance, entropy production rate and circulation distribution. We prove the equivalence of the following statements: The time-periodic Markov chain is periodically reversible; It is in detailed balance; Kolmogorov's cycle condition is satisfied; Its entropy production rate vanishes; Every circuit and its reversed circuit have the same circulation weight. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors, i.e. the existence of net circulation, can occur only in nonequilibrium and irreversible systems. Moreover, we verify the large deviation property and the Gallavotti-Cohen fluctuation theorem of sample entropy production rates of the Markov chain. Springer Science+Business Media, Inc., 2006 Brownian motor nationallicence time-periodic Markov chain nationallicence periodical reversibility nationallicence detailed balance nationallicence entropy production nationallicence circulation, fluctuation theorem nationallicence Ge Hao LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China aut Jiang Da-Quan LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China aut Qian Min LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/4(2006-05-01), 831-859 0022-4715 123:4<831 2006 123 10955 https://doi.org/10.1007/s10955-006-9099-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9099-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ge Hao LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China aut NATIONALLICENCE 700 1- Jiang Da-Quan LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China aut NATIONALLICENCE 700 1- Qian Min LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/4(2006-05-01), 831-859 0022-4715 123:4<831 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer