Abstract
In this paper, we establish a rigorous mathematical theory of three types of fluctuation-dissipation theorems (FDTs) for inhomogeneous Markov jump processes. It turns out that the FDTs and the response formula proved in this paper apply to any form of external perturbations and thus are quite general. Further physical and biochemical applications are also discussed. In particular, the FDTs are used to study an important biochemical phenomenon called adaptation.
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