Phenomenological coefficients in linear nonequilibrium thermodynamics have been considered to be independent, apart from restrictions due to the Onsager-Casimir reciprocal relations and the requirement to have non-negative entropy production. Recently, it has been shown that functional constraints between these coefficients may hold, restricting their dependence on state variables, especially in the case of coupled phenomena. Here we demonstrate that such restrictions require only mild assumptions on the system of interest and are, in fact, much more constraining than previously reported. Such constraints vastly reduce the set of plausible models for constitutive relations and allow for simpler experimental determinations of dependencies in coupled systems. These results may also clarify inconsistencies in the literature regarding constitutive models used that do not obey these thermodynamic constraints.

Department of Mathematics FNSPE Czech Technical University Prague Trojanova 13 Prague 2 12000 Czech Republic

Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter Woodstock Road Oxford OX2 6GG United Kingdom

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