动力学可观测量的对称诱导波动关系，无论其在时间反转下的行为如何
Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
摘要：
我们扩展以前的工作来描述一类波动关系（FR）出现的结果，在马尔可夫链的随机轨迹的水平上的对称性。我们证明，给定这样的对称性，并为一个合适的动态观察，它总是可以得到一个FR下有偏动态对应于所谓的广义Doob变换。我们考虑的动力学的一般变换超越了时间反演或空间等距性，这意味着无论时间反演下的行为如何，例如对于时间对称的可观测量而不是电流，都存在可观测量的FR。我们进一步展示了如何推导出在长时间的限制，这些FR从对称性的发电机的动态。我们用四个例子来说明我们的结果，这些例子突出了我们工作的新颖特征。
英文摘要：
We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behaviour under time-reversal, for example for time-symmetric observables rather than currents. We further show how to deduce in the long-time limit these FRs from the symmetry properties of the generator of the dynamics. We illustrate our results with four examples that highlight the novel features of our work.
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