Reciprocal relations between kinetic curves

@article{Yablonsky2010ReciprocalRB,
  title={Reciprocal relations between kinetic curves},
  author={G. S. Yablonsky and Alexander N Gorban and Denis Constales and Vladimir. V. Galvita and Guy B. Marin},
  journal={EPL (Europhysics Letters)},
  year={2010},
  volume={93},
  pages={20004}
}
We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, , the kinetic operator K is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, exp(Kt), is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the i-th pure state and measure the probability pj(t) of the j-th state (j≠i… 
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