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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.

Transport-theoretical derivation of the entropy production in relativistic binary mixtures of ideal fluids