Linear Thermodynamics and Phenomenological Coefficients

Abstract

It results from the equilibrium equalities (3.14), that in its neighbourhood, the link between the flows J_α and the forces X_α may be assumed to be linear:

$$$$

(4.1)

Such relations are called phenomenological laws, where the L_αβ denote the phenomenological coefficients. They include many empirical laws such as the Fourier’s law for the heat conduction, the Fick’s law for the diffusion, the Newton law for viscous fluids, and so on. The entropy production (3.6) takes here the quadratic form:

$$$$

(4.2)

implying the inequalities:

$$$$

(4.3)

Hence, the proper coefficients L_αα, L_ββ, have to be positive quantities. On the contrary the relations (4.1) are rarely useful in representing chemical kinetics, which belongs generally to the non-linear thermodynamics.