Entropy production for quasi-adiabatic parameter changes dominated by hydrodynamics

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 $t_{\text{r}}$.

13 pages, 5 figures

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