CSH Talk by Jan Korbel “Thermodynamics of exponential Kolmogorov-Nagumo averages”

Aug 25, 2023 | 15:0016:00

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Jan Korbel (CSH) will present a talk on Friday, August 25th, from 3 – 4 PM at the Salon.





Title: Thermodynamics of exponential Kolmogorov-Nagumo averages




Abstract: We investigate 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 Rényi’s entropy with parameter γ, 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 β that are suddenly quenched to another heat reservoir with inverse temperature β’ = (1-γ) β. 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.


Aug 25, 2023


Jan Korbel


Complexity Science Hub Vienna
Josefstaedter Straße 39
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