  The Barboza-Alcaniz EoS parametrization has been considered and its
$q$-parametrization has been investigated in search for a thermodynamic
motivation. For this, we have studied the validity of the generalized second
law of thermodynamics as well as the thermodynamic equilibrium considering the
cosmological apparent horizon as the boundary. Also, an expression for the
particle creation rate has been obtained in terms of $q$ assuming an adiabatic
particle creation scenario and its behavior has been studied for consistency
during various phases of evolution of the Universe as suggested by various
thermodynamic arguments found in the literature.
