  In this paper we propose the use of concepts from thermodynamics in the study
of crowd dynamics. Our continuous model consists of the continuity equation for
the density of the crowd and a kinetic equation for the velocity field. The
latter includes a nonlocal term that models interactions between individuals.
To support our modelling assumptions, we introduce an inequality that resembles
the Second Law of Thermodynamics, containing an entropy-like functional. We
show that its time derivative equals a positive dissipation term minus a
corrector term. The latter term should be small for the time derivative of the
entropy to be positive. In case of isotropic interactions the corrector term is
absent. For the anisotropic case, we support the claim that the corrector term
is small by simulations for the corresponding particle system. They reveal that
this term is sufficiently small for the entropy still to increase. Moreover, we
show that the entropy converges in time towards a limit value.
