On the thermodynamics of one-fluid Szekeres'like cosmologies

The thermodynamic behavior of the inhomogeneous Szekeres type cosmologies with a perfect fluids as source of gravitation is examined. Since the matter motion is geodetic, the absence of heat flow implies that the temperature is a function of time alone. For a subclass approaching homogeneity and isotropy at large cosmological times an expression for the temperature is derived. It does not coincide with the law of temperature satisfied by the FRW universes, even asymptotically. However, by assuming an equation of state explicitly dependent of the space coordinates, it is shown that the FRW thermodynamics may be recovered. In all cases the Euler and Gibbs-Duhem relations are no longer valid. (author)