  In this paper we demonstrate that Boltzmann's $H$-theorem does not
necessarily hold in the context of theories of gravity with nonminimally
coupled matter fields. We find sufficient conditions for the violation of
Boltzmann's $H$-theorem and derive an expression for the evolution of
Boltzmann's $H$ in terms of the nonminimal coupling function, valid in the case
of a collisionless gas in a homogeneous and isotropic
Friedmann-Lema\^itre-Robertson-Walker universe. We highlight the implications
of this result for the evolution of the entropy of the matter fields, briefly
discussing the role played by collisions between particles whenever they are
relevant. We also suggest a possible link between the high entropy of the
Universe and the weakness of gravity in the context of these theories.
