  We explore the possibility of gravitationally generated particle production
in the scalar-tensor representation of $f(R,T)$ gravity. Due to the explicit
nonminimal curvature-matter coupling in the theory, the divergence of the
matter energy-momentum tensor does not vanish. We explore the physical and
cosmological implications of this property by using the formalism of
irreversible thermodynamics of open systems in the presence of matter
creation/annihilation. The particle creation rates, pressure, temperature
evolution and the expression of the comoving entropy are obtained in a
covariant formulation and discussed in detail. Applied together with the
gravitational field equations, the thermodynamics of open systems lead to a
generalization of the standard $\Lambda$CDM cosmological paradigm, in which the
particle creation rates and pressures are effectively considered as components
of the cosmological fluid energy-momentum tensor. We also consider specific
models, and compare the scalar-tensor $f(R,T)$ cosmology with the $\Lambda$CDM
scenario and the observational data for the Hubble function. The properties of
the particle creation rates, of the creation pressures, and entropy generation
through gravitational matter production are further investigated in both the
low and high redshift limits.
