  We study the non-equilibrium dynamics of two tunnel-coupled one-dimensional
quasicondensates following a quench of the coupling strength from zero to a
fixed finite value. More specifically, starting from two independent
quasicondensates in thermal equilibrium, with initial temperature and chemical
potential imbalance, we suddenly switch on the tunnel-coupling and analyze the
post-quench equilibration in terms of particle number and energy imbalances. We
find that, in certain parameter regimes, the net energy can flow from the
colder quasicondensate to the hotter one and is governed by the surplus of low
energy particles flowing from the cold to the hot system relative to the
high-energy particles flowing in the reverse direction. In all cases, the
approach to the new thermal equilibrium occurs through transient, damped
oscillations. We also find that for a balanced initial state the coupled
quasicondensates can relax into a final thermal equilibrium state in which they
display a thermal phase coherence length that is larger than their initial
phase coherence length, even though the new equilibrium temperature is higher.
The increase in the phase coherence length occurs due to phase locking which
manifests itself via an increased degree of correlation between the local
relative phases of the quasicondensates at two arbitrary points.
