Abstract
An asymmetry in thermal relaxation toward equilibrium has been uncovered for Langevin systems near stable minima [Phys. Rev. Lett. 125, 110602 (2020)]. It has been shown that, given the same degree of nonequilibrium of the initial distributions, relaxation from a lower temperature state (heating) is faster than that from a higher temperature state (cooling). In this study, we elucidate this relaxation asymmetry for discrete-state Markovian systems described by the master equation. We rigorously prove that heating is faster than cooling for arbitrary two-state systems, whereas for systems with more than two distinct energy levels, the relaxation asymmetry is no longer universal. Furthermore, for systems whose energy levels degenerate into two energy states, we find that there exist critical thresholds of the energy gap. Depending on the magnitude of the energy gap, heating can be faster or slower than cooling, irrespective of the transition rates between states. Our results clarify the relaxation asymmetry for discrete-state systems and reveal several hidden features inherent in thermal relaxation.
Highlights
Systems attached to thermal reservoirs will relax toward a stationary state
We present our main results on the relaxation asymmetry, including numerical illustrations and proofs
We elucidated the relaxation asymmetry for discrete-state systems described by Markov jump processes
Summary
Systems attached to thermal reservoirs will relax toward a stationary state. Such thermal relaxation processes are ubiquitous in nature and possess rich properties from both dynamic and thermodynamic perspectives. By considering a pair of thermodynamically equidistant temperature quenches (which have the same nonequilibrium free energy difference), they unveiled an unforeseen asymmetry in thermal relaxation; i.e., relaxation from a lower temperature is faster than that from a higher temperature Speaking, it implies that heating up cold objects is faster than cooling down hot objects. Depending on whether the energy gap is larger or smaller than these thresholds, it can be concluded with certainty that heating is faster or slower than cooling These theoretical results are numerically demonstrated using several discrete-state systems. Let |pit be the time-evolution distribution corresponding to the initial state |π i , heating is said to be faster (slower) than cooling if. Because the sign of γni can be absorbed by changing the eigenvectors |vn → −|vn , hereafter, we assume γ2h 0, which implies that f 2|π h 0
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