Measure of the violation of the detailed balance criterion: A possible definition of a "distance" from equilibrium

Abstract

Motivated by the classification of nonequilibrium steady states suggested by R. K. P. Zia and B. Schmittmann, in J. Stat. Mech.1742-546810.1088/1742-5468/ 2007/07/P07012 (2007) P07012, we propose to measure the violation of the detailed balance criterion by the p norm (||K*||p) of the matrix formed by the probability currents. Its asymptotic analysis, for the totally asymmetric simple exclusion process, motivates the definition of a "distance" from equilibrium K* obtained for p=1. In addition, we show that the latter quantity and the average activity * are both related to the probability distribution of the entropy production. Finally, considering the open asymmetric simple exclusion process and open zero-range process, we show that the current of particles gives an exact measure of the violation of detailed balance. © 2011 American Physical Society.