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arXiv · 2309.16198

Adiabatic theorem for classical stochastic processes

Kazutaka Takahashi
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Abstract

We apply adiabatic theorems developed for quantum mechanics to stochastic annealing processes described by the classical master equation with a time-dependent generator. When the instantaneous stationary state is unique and the minimum decay rate g is nonzero, the time-evolved state is basically relaxed to the instantaneous stationary state. By formulating an asymptotic expansion rigorously, we derive conditions for the annealing time T that the state is close to the instantaneous stationary state. Depending on the time dependence of the generator, typical conditions are written as T> const/g^a with 1 const|ln g|/g^2.

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Kazutaka Takahashi. 2023-09-28. Adiabatic theorem for classical stochastic processes. https://doi.org/10.1088/1751-8121%2Fad3189

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