Onsager matrix for finite-time and weak processes

Pierre Nazé

Published 2023-05-08Version 1

Modeling of physical systems must be based on their suitability to unavoidable physical laws. In this work, in the context of classical, isothermal, finite-time, and weak drivings, I demonstrate that physical systems, driven simultaneously at the same rate in two or more external parameters, must have the Fourier transform of their relaxation functions composing a positive-definite matrix in order to satisfy the Second Law of Thermodynamics. By evaluating them in the limit of near-to-equilibrium processes, I identify that such coefficients are nothing more than the Onsager ones. The result is verified in paradigmatic models, where the extended Onsager matrices of the overdamped and underdamped white noise Brownian motions, driven simultaneously at the same rate in the stiffening and moving laser traps, are positive-definite.