Violation of local equilibrium thermodynamics in one-dimensional Hamiltonian-Potts model

TL;DR

This study demonstrates that local equilibrium thermodynamics breaks down in a one-dimensional Hamiltonian-Potts model with fractional derivatives, revealing stabilized metastable states and deviations at phase interfaces under steady heat conduction.

Contribution

The paper introduces a minimal one-dimensional model with fractional derivatives to study non-equilibrium phase coexistence and demonstrates the violation of local equilibrium thermodynamics.

Findings

Interface temperature deviates from equilibrium transition temperature.

Metastable states can be stabilized by steady heat current.

Quantitative agreement with global thermodynamics predictions.

Abstract

We investigate non-equilibrium phase coexistence associated with a first-order phase transition by numerically studying a one-dimensional Hamiltonian-Potts model with fractional spatial derivatives. The fractional derivative is introduced so as to reproduce the low-wavenumber density of states of the standard two-dimensional model, allowing phase coexistence to occur in a minimal one-dimensional setting under steady heat conduction. By imposing a constant heat flux through boundary heat baths, we observe stable coexistence of ordered and disordered phases separated by a stationary interface. We find that the temperature at the interface systematically deviates from the equilibrium transition temperature, demonstrating a clear violation of the local equilibrium description. This deviation indicates that equilibrium metastable states can be stabilized and controlled by a steady heat current. Furthermore, the interface temperature obtained in our simulations is in quantitative agreement with the prediction of global thermodynamics for non-equilibrium steady states. These results confirm that the breakdown of local equilibrium and the stabilization of metastable states are intrinsic features of non-equilibrium first-order phase transitions, independent of spatial dimensionality. Our study thus provides a minimal and controlled numerical model for exploring the fundamental limits of thermodynamic descriptions in non-equilibrium steady states.