Universal lower bounds on energy and momentum diffusion in liquids

TL;DR

This paper establishes a fundamental lower bound on the thermal diffusivity of liquids and supercritical fluids, linking it to universal physical constants, and reveals a correlation with the minimum kinematic viscosity across phase diagrams.

Contribution

It introduces a universal lower bound for thermal diffusivity based on fundamental constants and connects it to the minimum of kinematic viscosity, unifying energy and momentum diffusion limits.

Findings

Thermal diffusivity has a lower bound fixed by fundamental constants.

Experimental data supports the existence of this lower bound.

The lower bounds of thermal diffusivity and kinematic viscosity coincide at their minima.

Abstract

Thermal energy can be conducted by different mechanisms including by single particles or collective excitations. Thermal conductivity is system-specific and shows a richness of behaviors currently explored in different systems including insulators, strange metals and cuprate superconductors. Here, we show that despite the seeming complexity of thermal transport, the thermal diffusivity $\alpha$ of liquids and supercritical fluids has a lower bound which is fixed by fundamental physical constants for each system as $\alpha_m=\frac{1}{4\pi}\frac{\hbar}{\sqrt{m_em}}$, where $m_e$ and $m$ are electron and molecule masses. The newly introduced elementary thermal diffusivity has an absolute lower bound dependent on $\hbar$ and the proton-to-electron mass ratio only. We back up this result by a wide range of experimental data. We also show that theoretical minima of $\alpha$ coincide with the fundamental lower limit of kinematic viscosity $\nu_m$. Consistent with experiments, this points to a universal lower bound for two distinct properties, energy and momentum diffusion, and a surprising correlation between the two transport mechanisms at their minima. We observe that $\alpha_m$ gives the minimum on the phase diagram except in the vicinity of the critical point, whereas $\nu_m$ gives the minimum on the entire phase diagram.