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Recent studies have experienced the acceleration of convergence in Markovchain Monte Carlo methods implemented by the systems without detailed balancecondition (DBC). However, such advantage of the violation of DBC has not beenconfirmed in general. We investigate the effect of the absence of DBC on theconvergence toward equilibrium. Surprisingly, it is shown that the DBCviolation always makes the relaxation faster. Our result implies the existenceof a kind of thermodynamic inequality that connects the nonequilibrium processrelaxing toward steady state with the relaxation process which has the sameprobability distribution as its equilibrium state.

Violation of detailed balance accelerates relaxation