6 - Entropy and transport

Abstract

The entropy cannot be defined as an average of a microscopic dynamical function. The entropy production appears as a quadratic form in the Hermitian moments of all orders and of all tensorial characters. It involves an infinite number of variables. Vectors and traceless tensors do not couple to each other. The expression of the entropy production as a quadratic form in the Hermitian moments is an intrinsic one. The rate of entropy production is determined by the collisional relaxation times. The combination of entropy production and transport theory is obtained by introducing the transport equations, which relate the thermodynamic fluxes to the thermodynamic forces. The transport form of the entropy production determines the entropy production in terms of the external constraints driving the plasma, that is, the electric and magnetic fields and the gradients of temperature, pressure, and velocity. In contrast to the “kinetic form,” the transport form of the entropy production involves no explicit truncation level. The truncation level is contained in the values of the transport coefficients, which are evaluated in a given approximation.