  Entropy production during the process of thermal phase-separation of
multiphase flows is investigated by means of a discrete Boltzmann kinetic
model. The entropy production rate is found to increase during the spinodal
decomposition stage and to decrease during the domain growth stage, attaining
its maximum at the crossover between the two. Such behaviour provides a natural
criterion to identify and discriminate between the two regimes. Furthermore,
the effects of heat conductivity, viscosity and surface tension on the entropy
production rate are investigated by systematically probing the interplay
between non-equilibrium energy and momentum fluxes. It is found that the
entropy production rate due to energy fluxes is an increasing function of the
Prandtl number, while the momentum fluxes exhibit an opposite trend. On the
other hand, both contributions show an increasing trend with surface tension.
The present analysis inscribes within the general framework of non-equilibrium
thermodynamics and consequently it is expected to be relevant to a broad class
of soft-flowing systems far from mechanical and thermal equilibrium.
