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Entropy production for quasi-adiabatic parameter changes dominated by hydrodynamics
- Source :
- Phys. Rev. A 103, 033309 (2021)
- Publication Year :
- 2020
-
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 $t_\text{r}$.<br />Comment: 13 pages, 5 figures
- Subjects :
- Condensed Matter - Statistical Mechanics
Condensed Matter - Quantum Gases
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. A 103, 033309 (2021)
- Publication Type :
- Report
- Accession number :
- edsarx.2010.16163
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevA.103.033309