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arXiv · 2509.01714

Generalized Rényi Entropy Production Rate in Non-equilibrium Systems: From Markov Processes to Chaotic Dynamics

J. M. Nieto-Villar·R. Mansilla·I. Santamaria-Holek
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Abstract

A generalization of the entropy production rate is proposed $Π_q$ in non-equilibrium systems by extending the formalism of classical stochastic thermodynamics to regimes with non-Gaussian fluctuations. Through the Rényi entropy $S_q$ , where entropic parameter $q$ modulates critical fluctuations, it is defined $Π_q$ and the postulated generalized $q$-affinity ${\cal A}_q$ for Markov processes, where it is demonstrated that $Π_q \geq 0$, generalizing the second thermodynamics law.The derived formal framework was applied to the Rössler model, a nonlinear dynamical system exhibiting chaos. Numerical simulations show that the entropy production rate $Π_q$ can be used as an index of robustness and complexity by quantitatively corroborating the greater robustness of funnel-type chaos compared to spiral-type chaos. Our results reveal limitations of Gibbs-Shannon entropy in capturing non-Gaussian fluctuations induced by nonlinearity. On the contrary, it is found that $Π_q$ it can be a suitable magnitude to measure the intensity of chaotic dynamics through the entropy parameter $q$ , indicating a plausible link with Lyapunov exponents. The proposed formal framework extends the scope of stochastic thermodynamics to complex systems, integrating chaotic dynamics and the role of the entropic index q as a source of irreversibility and in capturing non-Gaussian contributions to entropy production.

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J. M. Nieto-Villar, R. Mansilla, I. Santamaria-Holek. 2025-10-01. Generalized Rényi Entropy Production Rate in Non-equilibrium Systems: From Markov Processes to Chaotic Dynamics. https://arxiv.org/abs/2509.01714

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