  We have studied the decoherence mechanism in a fermion and scalar quantum
field theory with the Yukawa interaction in the Minkowski spacetime, using the
non-equilibrium effective field theory formalism appropriate for open systems.
The scalar field is treated as the system whereas the fermions as the
environment. As the simplest realistic scenario, we assume that an observer
measures only the Gaussian 2-point correlator for the scalar field. The cause
of decoherence and the subsequent entropy generation is the ignorance of
information stored in higher-order correlators, Gaussian and non-Gaussian, of
the system and the surrounding. Using the 2-loop 2-particle irreducible
effective action, we construct the renormalised Kadanoff-Baym equations, i.e.,
the equation of motion satisfied by the 2-point correlators in the
Schwinger-Keldysh formalism. These equations contain the non-local self-energy
corrections. We then compute the statistical propagator in terms of the 2-point
functions. Using the relationship of the statistical propagator with the phase
space area, we next compute the von Neumann entropy for the system. We have
obtained the variation of the entropy with respect to various relevant
parameters. We also discuss the qualitative similarities and differences of our
results with the scenario when both the system and the environment are scalar
fields.
