  We consider the entropy and decoherence in fermionic quantum systems. By
making a Gaussian Ansatz for the density operator of a collection of fermions
we study statistical 2-point correlators and express the entropy of a system
fermion in terms of these correlators. In a simple case when a set of N
thermalised environmental fermionic oscillators interacts bi-linearly with the
system fermion we can study its time dependent entropy, which also represents a
quantitative measure for decoherence. We then consider a relativistic fermionic
quantum field theory and take a mass mixing term as a simple model for the
Yukawa interaction. It turns out that even in this Gaussian approximation, the
fermionic system decoheres quite effectively, such that in a large coupling and
high temperature regime the system field approaches the temperature of the
environmental fields.
