Adiabatic theorem for Markov jump processes.

Abstract

We present an elementary proof of the adiabatic theorem for Markov jump processes. This theorem, analogous to its quantum counterpart, states that a system starting from an instantaneous steady state remains in the instantaneous steady state if the transition rate matrix changes sufficiently slowly. Our approach adapts techniques from quantum adiabatic theorems while addressing the challenges posed by non-Hermitian dynamics. We highlight the unique properties of transition matrices that enable this proof, providing a more accessible foundation for understanding adiabatic behavior in Markov jump processes.