Calculation of the entropy from master equations with time-dependent transition probabilities

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Abstract
A general relation between the statistical entropy, given by a functional of the distribution function, and the thermodynamic entropies, defined by the heat exchange of the system, is established for models described by master equations with time-dependent transition probabilities. The result is consistent with that derived by Langer and Sethna [Phys. Rev. Lett. 61, 570 (1988)] by using thermodynamic arguments. The asymptotic form of this relation for a single two-level system, in the limit of a very slow cooling rate, is presented and discussed.

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