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We extend previous work to describe a class of fluctuation relations (FRs)that emerge as a consequence of symmetries at the level of stochastictrajectories in Markov chains. We prove that given such a symmetry, and for asuitable dynamical observable, it is always possible to obtain a FR under abiased dynamics corresponding to the so-called generalized Doob transform. Thegeneral transformations of the dynamics that we consider go beyondtime-reversal or spatial isometries, and an implication is the existence of FRsfor observables irrespective of their behaviour under time-reversal, forexample for time-symmetric observables rather than currents. We further showhow to deduce in the long-time limit these FRs from the symmetry properties ofthe generator of the dynamics. We illustrate our results with four examplesthat highlight the novel features of our work.

Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal