We discuss the consequences of a variant of the Hatano-Sasa relation in whicha non-stationary distribution is used in place of the usual stationary one. Wefirst show that this non-stationary distribution is related to a difference oftraffic between the direct and dual dynamics. With this formalism, we extendthe definition of the adiabatic and non-adiabatic entropies introduced by M.Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for thestationary case. We also obtain interesting second-law like inequalities fortransitions between non-stationary states.
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机译：我们讨论了Hatano-Sasa关系的一种变体的后果，其中使用了非平稳分布来代替通常的平稳分布。我们首先表明，这种非平稳分布与直接动力学和双重动力学之间的流量差异有关。通过这种形式主义，我们扩展了M.Esposito和C. Van den Broeck在Phys中引入的绝热和非绝热熵的定义。牧师104，090601（2010）。我们还获得了有趣的第二定律，如非平稳状态之间转换的不等式。
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