Abstract
By considering a thermodynamic force as gauge field, we extend constitutive equations of Onsager's non-equilibrium thermodynamics to non-linear equations. In Onsager's non-equilibrium thermodynamics, the thermodynamic force corresponds to a pure gauge, for which the constitutive equations are obtained by gauge fixing. If we extend the thermodynamic force from pure gauge to physical one, we obtain the non-linear constitutive equations of non-equilibrium thermodynamics.
Highlights
Onsager’s theory is the most important one in non-equilibrium thermodynamics with linear constitutive equations [1, 2], in which constitutive equations for currents are derived from the minimum energy dissipation principle
Sugamoto pointed out with his collaborators including the present author that thermodynamic force can be viewed as a gauge field [10]
If we describe aμ using parameter τ, we get non-equilibrium thermodynamical Lagrangian L as follows2: L(a, da )dτ dτ
Summary
Onsager’s theory is the most important one in non-equilibrium thermodynamics with linear constitutive equations [1, 2], in which constitutive equations for currents are derived from the minimum energy dissipation principle. Later on, this argument was supported by the path integral representation of the probability distribution [3, 4, 5, 6, 7]. In this paper we discuss this statement more definitely by means of gauge fixing, and derive the non-linear constitutive equation by adding the free action of the usual electromagnetism. In Appendix D, a simple example is derived in our model
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