Causal heat conduction contravening the fading memory paradigm

TL;DR

This paper introduces a causal heat conduction model that challenges the fading memory paradigm, impacting the understanding of thermohaline convection and nuclear burning stability with potential relativistic extensions.

Contribution

It presents a novel heat conduction model based on a heat kernel that violates the fading memory paradigm, affecting the modeling of thermal processes in complex systems.

Findings

The new model influences the behavior of thermohaline convection.

It affects the stability analysis of nuclear burning.

A relativistic version of the transport equation is proposed.

Abstract

We propose a causal heat conduction model based on a heat kernel violating the fading memory paradigm. The resulting transport equation produces an equation for the temperature. The model is applied to the discussion of two important issues such as the thermohaline convection and the nuclear burning (in)stability. In both cases the behaviour of the system appears to be strongly dependent on the transport equation assumed, bringing out the effects of our specific kernel on the final description of these problems. A possible relativistic version of the obtained transport equation is presented.