Curie theorem

We have managed to interpret the theorem of minimum entropy generation and the Onsager relations on the basis of the second law therefore, we can additionally explain the Curie symmetry principle in terms of equilibrium. Let us suppose that far from the equilibrium between flows and forces there are nonlinear relationships... 

The capabilities of MEIS and the models of kinetics and nonequilibrium thermodynamics were compared based on the theoretical analysis and concrete examples. The main MEIS advantage was shown to consist in simplicity of initial assumptions on the equilibrium of modeled processes, their possible description by using the autonomous differential equations and the monotonicity of characteristic thermodynamic functions. Simplicity of the assumptions and universality of the applied principles of equilibrium and extremality lead to the lack of need in special formalized descriptions that automatically satisfy the Gibbs phase rule, the Prigogine theorem, the Curie principle, and some other factors comparative simplicity of the applied mathematical apparatus (differential equations are replaced by algebraic and transcendent ones) and easiness of initial information preparation possibility of sufficiently complete consideration of specific features of the modeled phenomena. 

Making use of Eqs. (2) and (3) the condition for the equilibrium form dO = 0, dV = 0 leads to Wulff s rule (Gibbs-Curie-Wulff theorem [iii-v]) generalized by - Kaischew [i] to account for the crystal-substrate interaction ... 

At any temperature, x(T)/Xc gives the effective number of free spins and is related by the fluctuation-dissipation theorem to the sum of all static spin correlations. The complicated X(T)/Xc behavior in Fig. 17 thus points to disordered exchanges in the power-law regime below 40 °K the flat region 40 < T < 140 K suggests that some 8% are essentially free and follow the Curie law, Eq. (7) the T > 140 K regime... 

We also note that the vector or tensor responses (3.187), (3.189) depend only on the vector or tensor driving forces respectively. This fact is known in linear irreversible thermodynamics as the Curie principle [36, 80, 88, 89] (cf. discussion in [34, 38]). Present theory shows however, that this property follows from the isotropy of constitutive functions and from the representation theorems of such linear functions, see Appendix A.2, Eqs.(A.ll)-(A.13) and (A.57)-(A.59). But representation theorems for nonlinear isotropic constitutive functions [64, 65] show that the Curie principle is not valid generally. 

Taking into account certain restrictions originating from the symmetry properties of isotropic liquids at equilibrium (Curie s theorem), after some tensor algebra we obtain the Navier-Stokes equations for single-component atomic fluids. 

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