Emergent Thermodynamics in a Quenched Quantum Many-Body System

We study the statistics of the work done, fluctuation relations, and irreversible entropy production in a quantum many-body system subject to the sudden quench of a control parameter. By treating the quench as a thermodynamic transformation we show that the emergence of irreversibility in the nonequilibrium dynamics of closed many-body quantum systems can be accurately characterized. We demonstrate our ideas by considering a transverse quantum Ising model that is taken out of equilibrium by an instantaneous change of the transverse field.

Figure 1

Left: The irreversible entropy production for a series of quenches with amplitude $|{\lambda }_{\tau }-{\lambda }_0|=0.01$ at $\beta =100$ for several different ring sizes. The initial value of the transverse field ${\lambda }_0$ is shown on the $x$ axis. Right: The irreversible entropy production for the same series of quenches in a ring of $N=10000$ spins at various temperatures.