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arXiv · 2604.15000

Thermodynamic Geometry of Relaxation

Hao Wang·Li Zhao·Shuai Deng·Yu-Han Ma
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Abstract

While the geometry of equilibrium states and driven non-equilibrium processes is clearly understood, a geometric description for relaxation towards equilibrium is still lacking. Here, we propose a thermo-geometric measure based on the Rayleigh quotient, reformulating relaxation as a fundamental competition between entropic stiffness and frictional dissipation. Taking a van der Waals gas with two dissipation channels as an example, we explicitly demonstrate its relaxation landscape. Particularly, we find that upon approaching the critical temperature $T_c$, the slow-mode relaxation rate vanishes linearly as $\lambda_s \propto (T-T_c)/T_c$, indicating critical slowing down. This study completes the thermodynamic geometry framework, providing a general tool for characterizing the relaxation dynamics of complex systems.

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Hao Wang, Li Zhao, Shuai Deng, Yu-Han Ma. 2026-04-16. Thermodynamic Geometry of Relaxation. https://arxiv.org/abs/2604.15000

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