caa a22 4500 469108940 CHVBK 20180323133104.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF00420585 doi (NATIONALLICENCE)springer-10.1007/BF00420585 Montanaro Adriano Dipartimento di ‘Metodi e Modelli Matematici per le Scienze Applicate', via Belzoni, 7, 35131, Universitá di Padova, Italy aut Uniqueness theorems for the entropy in any differential body of complexity one [Elektronische Daten] [Adriano Montanaro] By using in an essential way a certain condition of mutual physical equivalence between admissible response functions for the heat flux, in a previous paper uniqueness theorems were proved for the response functions of the internal energy and of the equilibrium stress, in connection with differential bodies of complexity 1. It was then pointed out that the equality expressing the vanishing of the static internal dissipation uniquely determines the rate of entropy variation in terms of the rate of the internal energy variation and of the equilibrium stress. This paper shows, in a threefold manner, that the last result also holds if one does not impose the condition of physical equivalence. The first proof uses the assumption that the response functions are Euclidean invariant. The second proof uses (i) the weaker assumption of Galilean invariance and (ii) a greater degree of smoothness of the response function for the internal energy. Both of these proofs use an axiom postulating the possibility of putting the body in contact with a vacuum. The third proof of the uniqueness property for the entropy is independent of the isolation axiom and uses the assumptions of the second proof. Whereas any of the first two proofs is a consequence of the uniqueness theorem for the internal energy-proved here by using the afore-mentioned axiom-the third proof does not depend on this theorem. Rather, disregarding the above isolation axiom, it implies that uniqueness of the entropy is compatible with non-uniqueness of both the stress and internal energy. Kluwer Academic Publishers, 1992 Thermodynamics of solids nationallicence Continuum Mechanics nationallicence Constitutive equations nationallicence Meccanica Kluwer Academic Publishers 27/2(1992-06-01), 75-83 0025-6455 27:2<75 1992 27 11012 https://doi.org/10.1007/BF00420585 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00420585 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Montanaro Adriano Dipartimento di ‘Metodi e Modelli Matematici per le Scienze Applicate', via Belzoni, 7, 35131, Universitá di Padova, Italy aut NATIONALLICENCE 773 0- Meccanica Kluwer Academic Publishers 27/2(1992-06-01), 75-83 0025-6455 27:2<75 1992 27 11012 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer