  We consider how the occurrence of first-order phase transitions in
non-constant pressure differs from those at constant pressure. The former has
shown the non-linear phase structure of mixed matter, which implies a particle
number dependence of the binding energies of the two species. If the mixed
matter is mixed hadron-quark phase, nucleon outgoing from hadronic phase and
ingoing to quark phase probably reduces the system to a non-equilibrium state,
in other words, there exists the imbalance of the two phases when deconfinement
takes place. This novel non-equilibrium process is very analogous to the
nuclear reactions that nuclei emit neutrons and absorb them under appropriate
conditions. We present self-consistent thermodynamics in description for the
processes and identify the microphysics responsible for the processes. The
microphysics is an inevitable consequence of non-linear phase structure instead
of the effect of an additional dissipation force. When applying our findings to
the neutron star containing mixed hadron-quark matter, it is found that the
newly discovered energy release might strongly change the thermal evolution
behavior of the star.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena;Nuclear Theory