  In this work, we explore the formalism of the irreversible thermodynamics of
open systems and the possibility of gravitationally generated particle
production in modified gravity. More specifically, we consider the
scalar-tensor representation of $f(R,T)$ gravity, in which the matter
energy-momentum tensor is not conserved due to a nonminimal curvature-matter
coupling. In the context of the irreversible thermodynamics of open systems,
this non-conservation of the energy-momentum tensor can be interpreted as an
irreversible flow of energy from the gravitational sector to the matter sector,
which, in general, could result in particle creation. We obtain and discuss the
expressions for the particle creation rate, the creation pressure, and the
entropy and temperature evolutions. Applied together with the modified field
equations of scalar-tensor $f(R,T)$ gravity, the thermodynamics of open systems
lead to a generalization of the $\Lambda$CDM cosmological paradigm, in which
the particle creation rate and pressure are considered effectively as
components of the cosmological fluid energy-momentum tensor. Thus, generally,
modified theories of gravity in which these two quantities do not vanish
provide a macroscopic phenomenological description of particle production in
the cosmological fluid filling the Universe and also lead to the possibility of
cosmological models that start from empty conditions and gradually build up
matter and entropy.
