We describe the Lie group and the group representations associated to the
nonlinear Thermodynamic Coordinate Transformations (TCT). The TCT guarantee the
validity of the Thermodynamic Covariance Principle (TCP) : {\it The nonlinear
closure equations, i.e. the flux-force relations, everywhere and in particular
outside the Onsager region, must be covariant under TCT}. In other terms, the
fundamental laws of thermodynamics should be manifestly covariant under
transformations between the admissible thermodynamic forces, i.e. under TCT.
The TCP ensures the validity of the fundamental theorems for systems far from
equilibrium. The symmetry properties of a physical system are intimately
related to the conservation laws characterizing that system. Noether's theorem
gives a precise description of this relation. We derive the conserved
(thermodynamic) currents and, as an example of calculation, a simple system out
of equilibrium where the validity of TCP is imposed at the level of the kinetic
equations is also analyzed.Comment: 35 pages, 6 figure

Evslin, Jarah

Sonnino, Alberto

Sonnino, Giorgio

Steinbrecher, György

Tirapegui, Enrique

English

arXiv

Giorgio Sonnino

Jarah Evslin

Alberto Sonnino

György Steinbrecher

Enrique Tirapegui

Crossref

Symmetry group and group representations associated with the thermodynamic covariance principle

The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e. the flux-force relations) valid for thermodynamic systems out of Onsager's region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e. the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e. under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Evslin, JARAH J

DI-fusion

The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e., the flux-force relations) valid for thermodynamic systems out of Onsager's region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e., under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed

Steinbrecher, Gyorgy

Tirapegui Zurbano, Enrique

Repositorio Académico de la Universidad de Chile