Classical $\phi^4$ Lattice Field Theory in Strong Thermal Gradients

TL;DR

This paper investigates the behavior of classical $^4$ lattice field theory under thermal gradients, revealing how thermal conductivity varies with temperature and identifying the limits of linear response and local equilibrium.

Contribution

It provides the first detailed analysis of thermal transport and the breakdown of linear response in classical $^4$ theory under strong thermal gradients.

Findings

Thermal conductivity depends on temperature.

Non-linear temperature profiles emerge under strong gradients.

Linear response theory breaks down far from equilibrium.

Abstract

The dynamics of classical $\phi^4$ theory under weak and strong thermal gradients is studied. We obtain the thermal conductivity of the theory including its temperature dependence. Under moderately strong thermal gradients, the temperature profiles become visibly non-linear, yet the phenomenon can be understood using the linear response theory. When we move further away from equilibrium, we find that the linear response theory eventually breaks down, and the concept of local equilibrium also fails.