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 behavior 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.

中文翻译：

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动态观测对象的对称性引起的波动关系，无论其在时间逆转下的行为如何。

我们扩展先前的工作来描述一类波动关系（FR），这些波动关系是由于马尔可夫链中的随机轨迹级别上的对称性而出现的。我们证明给定这样的对称性，并且对于合适的动力学可观察到，它总是有可能在与所谓的广义Doob变换相对应的偏置动力学下获得FR。我们考虑的动力学的一般变换超出了时间反转或空间等距性，这意味着可观测对象的FR的存在，而不管它们在时间反转下的行为如何，例如时间对称的可观测对象而不是电流。我们进一步展示了如何从动力学生成器的对称特性中长期推断出这些FR。我们通过四个示例来说明我们的结果，这些示例突出了我们工作的新颖性。