Entropy production for quasi-adiabatic parameter changes dominated by hydrodynamics

TL;DR

This paper investigates how hydrodynamic fluctuations influence entropy production during slow parameter changes in many-particle systems, revealing dimension-dependent scaling laws and confirming predictions through classical gas simulations.

Contribution

It introduces a hydrodynamics-based framework for understanding entropy production scaling in quasi-adiabatic processes across different dimensions.

Findings

Entropy production scales as 1/√t_r in 1D

Entropy production scales as ln(t_r)/t_r in 2D

Higher dimensions show entropy production scaling as 1/t_r

Abstract

A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_\text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state preparation, $t_\text{r} \to \infty$, the entropy production vanishes. In systems with conservation laws, the approach to the adiabatic limit is hampered by hydrodynamic long-time tails, arising from the algebraically slow relaxation of hydrodynamic fluctuations. We argue that the entropy production $\Delta S$ of a diffusive system at finite temperature in one or two dimensions is governed by hydrodynamic modes resulting in $\Delta S \sim 1/\sqrt{t_\text{r}}$ in $d=1$ and $\Delta S \sim \ln(t_\text{r})/t_\text{r}$ in $d=2$. In higher dimensions, entropy production is instead dominated by other high-energy modes with $\Delta S \sim 1/t_\text{r}$. In order to verify the analytic prediction, we simulate the non-equilibrium dynamics of a classical two-component gas with point-like particles in one spatial dimension and examine the total entropy production as a function of $t_\text{r}$.