Summary
Starting from a tensorial local equilibrium axiom, in phenomenological relativistic nonequilibrium thermodynamics, we demonstrate for first-order approximation how a scalar local equilibrium axiom can be deduced. For the actual state, the scalar temperature and an inversetemperature 4-vectorβ μ can be defined, in this approximation. From the second-order approximation onwards, one cannot do it and the third-rank inverse-temperature tensorβ μϱσ must be used, from which we give a simple expression for the entropy source strength. Finally, we propose an operator of evolution, expressed fromβ μϱσ , that generalizes the Lie derivative with respect toβ μ, which would permit to use it in all the orders.
Riassunto
Partendo da un assioma tensoriale locale in equilibrio, nella termodinamica fenomenologica relativistica non in equilibrio, si dimostra per l'approssimazione di prim'ordine come un assioma scalare all'equilibrio locale può essere dedotto. Per lo stato attuale, la temperatura scalare ed un quadrivettore a temperatura inversaβ μ possono essere definiti in questa approssimazione. Dall'approssimazione di second'ordine in poi, non lo si può fare e si deve usare il tensore di temperatura inversa e terza classeβ μϱσ , dal quale si dà un'espressione semplice per la forza della sorgente di entropia. Infine si propone un operatore di evoluzione, espresso daβ μϱσ , che generalizza la derivata di Lie rispetto aβ μ, che permetterebbe di usarlo a tutti gli ordini.
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Gariel, J. Tensorial local-equilibrium axiom and operator of evolution. Nuov Cim B 94, 119–139 (1986). https://doi.org/10.1007/BF02759752
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DOI: https://doi.org/10.1007/BF02759752