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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.
Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field. The treatment in that work was limited to a four-dimensional Minkowksi space-time
Phenomenological equations describing the Seebeck, Hall, Nernst, Peltier, Ettingshausen, and Righi-Leduc effects are numerically solved for the temperature, electric current, and electrochemical potential distributions of semiconductors under magnetic field. The results are compared to experiments.
The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is show
The introduction of electromagnetic fields into the Boltzmann equation following a 5D general relativistic approach is considered in order to establish the transport equations for dilute charged fluids in the presence of a weak electromagnetic field.
We show that, in the context of the two-field measure theory, any k-essence model leads to the existence of a fluid made of non-relativistic matter and cosmological constant that would explain the dark matter and dark energy problem at the same time.