A Note on Rényi Entropy Production for Markovian Evolution

Entropy production in stochastic thermodynamics is defined as the average over all the possible system trajectories of a quantity (observable) which measures the divergence between a trajectory and its time-reversal. In this way a quantitative measure of the irreversible evolution of a system out of equilibrium can be given. In this note we consider a Markov system and substitute the linear average with a more general notion of average over the trajectories (Kolmogorov-Nagumo mean) which corresponds to substituting Shannon entropy with Rény entropy. We show that, unlike the linear average case, the resulting notion of entropy production depends on how the observable is defined.