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Mean-field convective phase separation under thermal gradients

Meander Van den Brande1, François Huveneers1, and Kyosuke Adachi2,3

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Phys. Rev. E 114, L042107 – Published 20 October, 2026

DOI: https://doi.org/10.1103/fdfm-njx6

Abstract

Nonequilibrium conditions fundamentally change how systems undergo phase separation. In lattice gases with attractive interactions under temperature gradients, particles have been shown to form periodic patterns and steady convective currents; however, a clear theoretical explanation of this convective phase separation is still missing. Here we present a dynamical mean-field model that describes the mechanism behind this convective phase separation. Using linear stability analysis, we show that the transition from a uniform state to a periodic pattern is driven by the emergence of a dominant unstable mode. Numerical simulations confirm the predicted phase diagram and demonstrate that these convective currents are a robust feature of the steady state, appearing regardless of the initial conditions. These results provide a direct approach for understanding how temperature gradients drive the formation of steady-state convective patterns.

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Phys. Rev. E 114, L042107– Published 20 October, 2026
  • Received 6 March 2026
  • Accepted 1 October 2026
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