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Colloquium on Gauge Transformations for Thermodynamic Fluxesand Thermal Diffusion
1  Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
2  Institute of Continuous Media Mechanics, UB RAS, Perm 614013, Russia

Abstract: We discuss the molecular diffusion transport in infinitely dilute liquid solutions under non-isothermal conditions.  This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of chemical potential in the presence of temperature gradient.  The transport equations contain the contributions owned by a gauge transformation related to the fact that chemical potential is determined up to the summand of form (AT+B) with arbitrary constants A and B, where constant A is owned by the entropy invariance with respect to shifts by a constant value and B is owned by the potential energy invariance with respect to shifts by a constant value.  The coefficients of the cross-effect terms in thermodynamic fluxes are contributed by this gauge transformation and, generally, are not the actual cross-effect physical transport coefficients.  Our treatment is based on consideration of the entropy balance and suggests a promising hint for attempts of evaluation of the thermal diffusion constant from the first principles.  We also discuss the impossibility of the "barodiffusion" for dilute solutions, understood in a sense of diffusion flux driven by the pressure gradient itself.  When one speaks of "barodiffusion" terms in literature, these terms typically represent the drift in external potential force field (e.g., electric or gravitational fields), where in the final equations the specific force on molecules is substituted with an expression with the hydrostatic pressure gradient this external force field produces.  Obviously, the interpretation of the latter as "barodiffusion" is fragile and may hinder the accounting for the diffusion fluxes produced by the pressure gradient itself.
Keywords: Dilute solutions; thermodynamic transport cross-effects; thermal diffusion