Variational multi-fluid dynamics and causal heat conductivity

Abstract

We discuss heat conductivity from the point of view of a variational multi-fluid model, treating entropy as a dynamical entity. We demonstrate that a two-fluid model with a massive fluid component and a massless entropy can reproduce a number of key results from extended irreversible thermodynamics. In particular, we show that the entropy entrainment is intimately linked to the thermal-relaxation time that is required to make heat propagation in solids causal. We also discuss non-local terms that arise naturally in a dissipative multi-fluid model, and relate these terms to those of phonon hydrodynamics. Finally, we formulate a complete heat-conducting two-component model and discuss briefly the new dissipative terms that arise.

Thermal dynamics in general relativity

“…The simpler context of our analysis serves to clarify the main points. Finally, we worked out the non-relativistic limit of our results, making contact with the recent work of Andersson & Comer (2010). This essentially completes the picture, and we now have a consistent framework for discussing causal heat conductivity in both Newtonian and relativistic dynamics.…”

“…An important aspect of the present work is that it extends the recent Newtonian model of thermal dynamics discussed by Andersson & Comer (2010) to general relativity. In both cases, entrainment has a fundamental impact on the dynamics of entropy.…”

“…The result is then compared with the predictions of the Israel and Stewart model. The Newtonian limit of the theory is obtained in §4, which establishes the close connection to the nonrelativistic model of Andersson & Comer (2010). The paper concludes with a brief discussion of the implications of the results, possible future extensions and applications.…”

“…For the massless entropy, it is easy to see that we get (4.21) We have arrived at the Newtonian two-fluid point model that was taken as the starting point by Andersson & Comer (2010). In other words, their Newtonian model is the natural non-relativistic counterpart to the model developed in §2.…”

A variational approach to resistive relativistic plasmas

“…Notice also how the inclusion of n 2 xy has led to so-called "entrainment", a tilting of the fluid momenta in the sense that µ x a is no longer simply proportional to its own flux n a x . Entrainment [21][22][23][24] between neutrons and protons is generally thought to be important in superfluid neutron stars and entrainment between matter and entropy can be shown to be important for causal heat conductivity [25].…”