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The second law of thermodynamics states that entropy production cannot benegative. Recent developments concerning uncertainty relations in stochasticthermodynamics, such as thermodynamic uncertainty relations and speed limits,have yielded refined second laws that provide lower bounds of entropyproduction by incorporating information from current statistics ordistributions. In contrast, in this study, we bound the entropy production fromabove by terms comprising the dynamical activity and maximum transition-rateratio. We derive two upper bounds: one applies to steady-state conditions,whereas the other applies to arbitrary time-dependent conditions. We verifythese bounds through numerical simulation and identify several potentialapplications.

Upper bound for entropy production in Markov processes