违反“细致平衡”标准的一种度量：离平衡“距离”的一种可能定义
A measure of the violation of the 'detailed balance' criterion: a possible definition of a 'distance' from equilibrium
摘要：
受R. K. P. Zia和B. Schmittmann，J. Stat. P07012（2007）中，我们提出通过概率流形成的矩阵的$p$ -范数（$||K||_p$）来测量对“细致平衡”准则的违反。它的渐近分析，完全不对称的排斥过程，激发了一个“距离”的定义，从平衡$K^*$获得$p=1$。此外，我们表明，后者的数量和平均活动$A^*$都与熵产生的概率分布。最后，考虑到开放ASEP和开放ZRP，我们表明，粒子的电流给出了一个精确的措施违反“细致平衡”。
英文摘要：
Motivated by the classification of non-equilibrium steady states suggested by R.K.P. Zia and B. Schmittmann in J. Stat. Mech. P07012 (2007), 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 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 $A^*$ are both related to the probability distribution of the entropy production. Finally, considering the open-ASEP and open-ZRP, we show that the current of particles gives an exact measure of the violation of 'detailed balance'.
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