  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 to satisfy the Second Law of
Thermodynamics. By evaluating them in the limit of near-to-equilibrium
processes, I identify that such coefficients are the Casimir-Onsager ones. The
result is verified in paradigmatic models of the overdamped and underdamped
white noise Brownian motions. Finally, an extension to thermally isolated
systems is made by using the time-averaged Casimir-Onsager matrix, in which the
example of the harmonic oscillator is presented.
