Heat~dissipation~in relativistic single charged fluids

When the temperature of a fluid is increased its out of equilibrium behavior is significantly modified. In particular kinetic theory predicts that~the heat~flux is not solely driven by a temperature gradient but can also be coupled to other thermodynamic vector forces. We explore the nature of~heat~conduction in a single component charged fluid in special relativity, where the electromagnetic field is introduced as an external force. We obtain an electrothermal effect, similar to the mixture's cross-effect, which is not present in the non-relativistic simple fluid. The general lines of the corresponding calculation will be shown, emphasizing the importance of reference frame invariance and the origin of the extra~heat~sources, in particular the role of the modified inertia and the difference in fluid's and molecules' proper times. The constitutive equation for the heat flux obtained using Chapman-Enskog's expansion in Marle's approximation will be analyzed together with the corresponding transport coefficients.The impact of this effect in the overall dynamics of the system here considered will be briefly discussed.