Thermodynamics of exponential Kolmogorov-Nagumo averages

This paper investigates generalized thermodynamic relationships in physical systems where relevant macroscopic variables are determined by the exponential Kolmogorov-Nagumo average. We show that while the thermodynamic entropy of such systems is naturally described by Renyi's entropy with parameter gamma, an ordinary Boltzmann distribution still describes their statistics under equilibrium thermodynamics. Our results show that systems described by exponential Kolmogorov-Nagumo averages can be interpreted as systems originally in thermal equilibrium with a heat reservoir with inverse temperature beta that are suddenly quenched to another heat reservoir with inverse temperature beta ' = (1 - gamma)beta. Furthermore, we show the connection with multifractal thermodynamics. For the non-equilibrium case, we show that the dynamics of systems described by exponential Kolmogorov-Nagumo averages still observe a second law of thermodynamics and the H-theorem. We further discuss the applications of stochastic thermodynamics in those systems-namely, the validity of fluctuation theorems-and the connection with thermodynamic length.

Automated summary

This paper investigates generalized thermodynamic relationships in physical systems where relevant macroscopic variables are determined by the exponential Kolmogorov-Nagumo average. The study shows that while the thermodynamic entropy of such systems is naturally described by Renyi's entropy with parameter gamma, an ordinary Boltzmann distribution still describes their statistics under equilibrium thermodynamics. Furthermore, the paper explores the connection with multifractal thermodynamics and demonstrates the validity of the second law of thermodynamics and the H-theorem in the dynamics of systems described by exponential Kolmogorov-Nagumo averages.