Non-equilibrium thermodynamics in f(R, T) gravity and dark energy

Modifying general relativity may be a suitable approach to solve the dark energy problem. Among the various theories of modified gravity, we consider the f(R, T) gravity, in which R is the Ricci scalar and T is the trace of the energy-momentum tensor. As an intriguing property, the conservation equation does not hold in f(R, T) gravity. It means that the divergence of the energy-momentum tensor does not vanish. Using the formalism of irreversible thermodynamics of open systems in the presence of matter creation or matter annihilation, one can explore the physical interpretation of non-conservative energy-momentum tensor. Comparing the non-conservative energy-momentum tensor in f(R, T) gravity with the one in an irreversible open system, one may conclude that there may be a flow of energy from the gravitational sector to the matter sector, which may result in matter creation. In this paper, we study the f(R, T) gravity in the presence of the ordinary matter and the scalar field from the viewpoint of the irreversible thermodynamics of open systems to explore the possibility of matter creation. The matter creation rate, the creation pressure, the entropy production rate and the temperature evolution can be obtained. This possible matter creation in f(R, T) gravity can be considered as a component of energy which may play the role of dark energy in the recent accelerated expanding phase of the Universe.