An Introduction to Stochastic Thermodynamics: From Basic to Advanced by Naoto Shiraishi

Author:Naoto Shiraishi
Language: eng
Format: epub, pdf
ISBN: 9789811981869
Publisher: Springer Nature Singapore

(10.7)

We denote the value of at by . In the following, we change only a parameter , and other parameters in are fixed (i.e., only edges are perturbed) otherwise explicitly noted.

We introduce an informed force at for as

(10.8)

where we defined as the stationary distribution of the state i with the parameter . The last equality follows from for . The distribution for a given is given as follows: For given , we consider a system with with removing all edges in . Its stationary distribution is defined as .

The term “informed" comes from the fact that in order to compute , we need to know the transition rate at different from the present transition rate at . Since we perturb edges only in , holds for and hence the transition rate R with edges not in is independent of (i.e., ). Using the informed force, we introduce the informed partial entropy production 3:

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