Scaling laws and bulk-boundary decoupling in heat flow

Abstract

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows to measure for the first time the marginal anomaly of the heat conductivity predicted for hard disks.

5 pages + 5 figures + 3 pages of supplementary material

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• The large deviation approach to statistical mechanics
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• Symmetries in Fluctuations Far from Equilibrium
• Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
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Cited by in corpus (5)

• A violation of universality in anomalous Fourier's law
• Probing local equilibrium in nonequilibrium fluids
• Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state
• Molecular hints of two-step transition to convective flow via streamline percolation
• Heat Conduction in a hard disc system with non-conserved momentum