Quantum thermodynamics of strongly correlated systems

We study tunneling quenches when a hot many-body quantum system is brought into instantaneous contact with a cold many-body quantum system. The dynamics of such systems can be understood as a combination of early-time von Neumann entropy gain and late-time energy relaxation. We show that at the shortest timescales there is an energy increase in each system linked to the entropy gain and supported by the collective binding energy between the systems. Counterintuitively to the classical expectation, this implies that also the hotter of the two subsystems generically experiences an initial energy increase when brought into contact with a colder system. We explain this early time energy gain with a quantum thermodynamical relation that holds even for systems out of equilibrium and, in the limit where the energy relaxation overwhelms the quantum correlation build-up, reduces to classical behavior. We use both, strongly correlated SYK systems and mixed field Ising chains with a tunneling quench to exhibit these characteristics and study the contribution of quantum correlations to the von Neumann entropy. Interestingly, we discover that the energy dynamics of an Ising model around the quantum critical point have similar qualitative behavior to a strongly interacting SYK system.