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By considering general Markov stochastic dynamics and its coarse-graining, westudy the framework of stochastic thermodynamics for the original and reduceddescriptions corresponding to different scales. We are especially concernedwith the case where the irreversible entropy production has a finite differencebetween the scales. We find that the sum of increment of nonequilibrium entropyand excess part of entropy production, which are key quantities in constructionof steady state thermodynamics, is essentially kept invariant with respect tothe change in the scales of description. This general result justifiesexperimental approaches toward steady state thermodynamics based oncoarse-grained variables. We demonstrate our result in a mesoscopic heat enginesystem.

Invariance of Steady State Thermodynamics between Different Scales of Description