Category Archives: hydrodynamics

Taming nonlinear energy diffusion: The case of time-crystal energy condensates

P.I. Hurtado, G. Cortés-Guillén

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.

Phys. Rev. E 114, 034110 (2026); arXiv:2607.07325

Scaling laws for stationary Navier-Stokes-Fourier flows and the unreasonable effectiveness of hydrodynamics at the molecular level

P.I. Hurtado, J. J. del Pozo, P. L. Garrido

Hydrodynamics provides a universal description of the emergent collective dynamics of vastly different many-body systems, based solely on their symmetries and conservation laws. Here we harness this universality, encoded in the Navier-Stokes-Fourier (NSF) equations, to find general scaling laws for the stationary uniaxial solutions of the compressible NSF problem far from equilibrium. We show for general transport coefficients that the steady density and temperature fields are functions of the pressure and a kinetic field that quantifies the quadratic excess velocity relative to the ratio of heat flux and shear stress. This kinetic field obeys in turn a spatial scaling law controlled by pressure and stress, which is inherited by the stationary density and temperature fields. We develop a scaling approach to measure the associated master curves, and confirm our predictions through compelling data collapses in large-scale molecular dynamics simulations of paradigmatic model fluids. Interestingly, the robustness of the scaling laws in the face of significant finite-size effects reveals the surprising accuracy of NSF equations in describing molecular-scale stationary flows. Overall, these scaling laws provide a novel characterization of stationary states in driven fluids.

arXiv:2512.13205