Taming nonlinear energy diffusion: The case of time-crystal energy condensates
Phys. Rev. E 114, 034110 – Published 8 September, 2026
DOI: https://doi.org/10.1103/dqjr-rp6k
Abstract
We study a bulk-driven nonlinear variant of the Kipnis-Marchioro-Presutti model of stochastic energy diffusion in which local collisions are biased to induce a net energy flow, resembling the effect of an external field. Starting from the microscopic master equation, we derive the hydrodynamic description of the driven system via a local equilibrium approximation, obtaining explicit expressions for the energy current and the associated diffusivity and mobility transport coefficients, which are nonlinear functions of the local energy density. We test our findings in kinetic Monte Carlo simulations of the model, and, as a proof of concept, we demonstrate the versatility of this driving mechanism to control nonlinear energy transport by inducing time-crystalline phases. In particular, we show that appropriately designed packing fields induce the spontaneous formation of traveling energy condensates, exhibiting robust long-range temporal order reminiscent of continuous time crystals. Our results provide a simple yet powerful framework to study bulk-driven nonlinear energy diffusion in stochastic many-body systems, offering a bridge between microscopic dynamics, macroscopic transport, and controlled spatiotemporal order.
Physics Subject Headings (PhySH)
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This article appears in the following collection:
Controlling Stochastic Dynamics Across Scales
We present a Collection of papers on Controlling Stochastic Dynamics Across Scales. It seeks to highlight novel studies on controlling the dynamics of complex stochastic systems with a rich phenomenology. Guest editors of the Collection are Étienne Fodor of the University of Luxembourg and Todd Gingrich of Northwestern University.
