Entropy Production in Relativistic Binary Mixtures

In this paper we calculate the entropy production of a relativistic binary mixture of inert dilute gases using kinetic theory. For this purpose we use the covariant form of Boltzmann's equation which, when suitably transformed, yields a formal expression for such quantity. Its physical meaning is extracted when the distribution function is expanded in the gradients using the well-known Chapman-Enskog method. Retaining the terms to first order, consistently with Linear Irreversible Thermodynamics we show that indeed, the entropy production can be expressed as a bilinear form of products between the fluxes and their corresponding forces. The implications of this result are thoroughly discussed

Relaxation time for the temperature in a dilute binary mixture from classical kinetic theory

The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the hypothesis of partial local equilibrium for both species. Neither a diffusion force nor mass diffusion appears in the system. We also estimate the time in which the temperatures of the components reach the full local equilibrium. In solving the Boltzmann equation, we imposed no assumptions on the collision term. We work out its solution by using the well known Chapman-Enskog method to first order in the gradients. The time in which the temperatures relax is obtained following Landau's original idea. The result is that the relaxation time for the temperatures is much smaller than the characteristic hydrodynamical times but greater than a collisional time. The main conclusion is that there is no need to study binary mixtures with different temperatures when hydrodynamical properties are sought