  The dynamics when a hot many-body quantum system is brought into
instantaneous contact with a cold many-body quantum system can be understood as
a combination of early time quantum correlation (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, even though
equilibrium thermodynamics does not apply. This energy increase is of quantum
origin and results from the collective binding energy between the two systems.
Counter-intuitively, this implies that also the hotter of the two systems
generically experiences an initial energy increase when brought into contact
with the other colder system. In the limit where the energy relaxation
overwhelms the (quantum) correlation build-up, classical energy dynamics
emerges where the energy in the hot system decreases immediately upon contact
with a cooler system. We use both strongly correlated SYK systems and weakly
correlated mixed field Ising chains to exhibit these characteristics, and
comment on its implications for both black hole evaporation and quantum
thermodynamics.
