Entropy production for quasiadiabatic parameter changes dominated by hydrodynamics

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