Thermoelectric and Thermomagnetic Effects in Kaluza’s Kinetic Theory
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Alma R. Sagaceta-Mejía
Abstract
A five-dimensional treatment of the Boltzmann equation is used to establish the constitutive equations that relate thermodynamic fluxes and forces up to first order in the gradients for simple charged fluids in the presence of electromagnetic fields. The formalism uses the ansatz first introduced by Kaluza back in 1921, proposing that the particle charge–mass ratio is proportional to the fifth component of its velocity field. It is shown that in this approach, space–time curvature yields thermodynamic forces leading to generalizations of the well-known cross-effects present in linear irreversible thermodynamics.
A Appendix
In this appendix we establish the conservation relations given by eq. (8) in a 5D space–time. The starting point is the Boltzmann equation given by
Multiplying both sides by the collisional invariant
In order to derive eq. (8), we make use of the identity
such that eq. (38) reads
The first term on the right-hand side is readily identified as
where
which can be shown to be of second order, and thus negligible, in Kaluza’s classical formalism by direct calculation of the Christoffel symbols using the metric tensor given in eq. (4). Using this fact in eq. (39) leads directly to expression (8) in the main text.
Acknowledgements:
The authors wish to thank Dominique Brun-Battistini for her valuable comments to this work.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Linear Irreversible Phenomenological Thermodynamics of Polarization Processes in Rigid Unmagnetic Insulators
- The Micromorphic Approach to Generalized Heat Equations
- The Rule of Temperature Coefficients for Selection of Optimal Separation Sequence for Multicomponent Mixtures in Thermal Systems
- Non-equilibrium Thermodynamical Description of Superfluid Transition in Liquid Helium
- Thermoelectric and Thermomagnetic Effects in Kaluza’s Kinetic Theory
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Linear Irreversible Phenomenological Thermodynamics of Polarization Processes in Rigid Unmagnetic Insulators
- The Micromorphic Approach to Generalized Heat Equations
- The Rule of Temperature Coefficients for Selection of Optimal Separation Sequence for Multicomponent Mixtures in Thermal Systems
- Non-equilibrium Thermodynamical Description of Superfluid Transition in Liquid Helium
- Thermoelectric and Thermomagnetic Effects in Kaluza’s Kinetic Theory
