Thermodynamics of exponential Kolmogorov-Nagumo averages

Abstract

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 Rényi'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 ${\beta }^{\prime }=(1-\gamma )\beta$. 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. namic length.

arXiv comment14 pages, 1 table. arXiv admin note: text overlap with arXiv:2203.13673. Authors note: the original manuscript arXiv:2203.13673 was splitted into two different manuscripts

References in corpus (32)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• Measuring thermodynamic length
• Three detailed fluctuation theorems
• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• The Gravity Dual of Renyi Entropy
• Holographic entanglement beyond classical gravity
• Renyi's information transfer between financial time series
• Measuring multivariate redundant information with pointwise common change in surprisal
• Maximum Entropy Principle in statistical inference: case for non-Shannonian entropies
• Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
• Geometry of escort distributions
• Renyi Entropy and Free Energy
• Shannon and Rényi mutual information in quantum critical spin chains
• On observability of Renyi's entropy
• Generalised exponential families and associated entropy functions
• Detecting Classical Phase Transitions with Renyi Mutual Information
• Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures using piecewise log-sum-exp inequalities
• Thermostatistics based on Kolmogorov-Nagumo averages: Unifying framework for extensive and nonextensive generalizations
• Generalized entropies and logarithms and their duality relations
• Multifractal Diffusion Entropy Analysis: Optimal Bin Width of Probability Histograms
• Geometric mutual information at classical critical points
• One-parameter class of uncertainty relations based on entropy power
• On the way towards a generalized entropy maximization procedure
• Unifying Aspects of Generalized Calculus
• Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory
• Consistency of the structure of Legendre transform in thermodynamics with the Kolmogorov-Nagumo average
• Information geometric duality of $\varphi$-deformed exponential families
• Information geometry of scaling expansions of non-exponentially growing configuration spaces
• Stochastic thermodynamics and fluctuation theorems for non-linear systems
• Thermodynamics of Markov Processes with Non-extensive Entropy and Free Energy
• Geometric Structures Induced by Deformations of the Legendre Transform

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• Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory
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• On nonlinear compression costs: when Shannon meets Rényi
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