  The theoretical and observational consequences of thermodynamics of open
systems, which allow particle creation are investigated in modified $f(R,T)$
($R$ is the Ricci scalar and $T$ is the trace of energy-momentum tensor) theory
of gravity within the framework of a flat Friedmann-Robertson-Walker line
element. A simplest particular model $f(R,T)=R+2f(T)$ and "gamma-law" equation
of state $p=(\gamma-1)\rho$ are assumed to explore the role of particle
creation in the early and late time evolution of the universe. A power-law
expansion model is proposed for $0\leq \gamma \leq 2$ by considering the
natural phenomenological particle creation rate $\psi=3\beta nH$, where $\beta$
is a pure number of the order of unity. A Big Rip singularity is observed for
$\gamma<0$, which describes the phantom cosmology. We observe that the
accelerated expansion of the universe is driven by the particle creation
without any exotic "quintessence" component or a cosmological constant. It is
also found by density parameter that the model becomes of negative curvature
due to particle creation and the entropy increases with the evolution of the
universe. Some kinematics tests such as lookback time, luminosity distance,
proper distance, angular diameter versus redshift are discussed in detail to
observe the role of particle creation in early and late time evolution of the
universe.
