Phase transition in the KMP model with Slow/Fast boundaries

TL;DR

This paper investigates a generalized KMP model with variable boundary exchange rates, demonstrating a phase transition in heat flow depending on these rates, which advances understanding of non-equilibrium statistical mechanics.

Contribution

It introduces a generalized KMP model with different boundary exchange rates and proves the existence of a phase transition in heat flow.

Findings

Existence of a phase transition in heat flow.

Boundary exchange rates critically influence the phase behavior.

Generalization extends understanding of non-equilibrium systems.

Abstract

The Kipnis-Marchioro-Presutti (KMP) is a known model consisting on a one-dimensional chain of mechanically uncoupled oscillators, whose interactions occur via independent Poisson clocks: when a Poisson clock rings, the total energy at two neighbors is redistributed uniformly at random between them. Moreover, at the boundaries, energy is exchanged with reservoirs of fixed temperatures. We study here a generalization of the KMP model by considering different rates at energy is exchanged with the reservoirs, and we then prove the existence of a phase transition for the heat flow.