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We examine the consistency of the thermodynamics of irrotational andnon-isentropic perfect fluids complying with matter conservation by looking atthe integrability conditions of the Gibbs-Duhem relation. We show that thelatter is always integrable for fluids of the following types: (a) static, (b)isentropic (admits a barotropic equation of state), (c) the source of aspacetime for which $r\ge 2$, where $r$ is the dimension of the orbit of theisometry group. This consistency scheme is tested also in two large classes ofknown exact solutions for which $r< 2$, in general: perfect fluid Szekeressolutions (classes I and II). In none of these cases, the Gibbs-Duhem relationis integrable, in general, though specific particular cases of Szekeres classII (all complying with $r<2$) are identified for which the integrability ofthis relation can be achieved. We show that Szekeres class I solutions satisfythe integrability conditions only in two trivial cases, namely the sphericallysymmetric limiting case and the Friedman-Roberson-Walker (FRW) cosmology.Explicit forms of the state variables and equations of state linking them aregiven explicitly and discussed in relation to the FRW limits of the solutions.We show that fixing free parameters in these solutions by a formalidentification with FRW parameters leads, in all cases examined, to unphysicaltemperature evolution laws, quite unrelated to those of their FRW limitingcosmologies.Comment: 29 pages, Plain.Te

On the thermodynamics of simple non-isentropic perfect fluids in general relativity