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

Crowds reaching targets by maximizing entropy: a Clausius-Duhem inequality approach