2025/09/01 by J.M. Nieto‐Villar, Nieto-Villar, J. M., Ricardo Mansilla +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2509.01714
openalex publication_date 2025/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalization of the entropy production rate is proposed Πq in non-equilibrium systems by extending the formalism of classical stochastic thermodynamics to regimes with non-Gaussian fluctuations. Through the Rényi entropy Sq , where entropic parameter q modulates critical fluctuations, it is defined Πq and the postulated generalized q-affinity \cal Aq for Markov processes, where it is demonstrated that Πq ≥ 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 Πq 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 Πq 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.