  As previously demonstrated, the entropy production -- a key quantity
characterizing the irreversibility of thermodynamic processes -- is related to
generation of correlations between degrees of freedom of the system and its
thermal environment. This raises the question of whether such correlations are
of a classical or quantum nature, namely, whether they are accessible through
local measurements on the correlated degrees of freedom. We address this
problem by considering fermionic and bosonic Gaussian systems. We show that for
fermions the entropy production is mostly quantum due to the parity
superselection rule which restricts the set of physically allowed measurements
to projections on the Fock states, thus significantly limiting the amount of
classically accessible correlations. In contrast, in bosonic systems a much
larger amount of correlations can be accessed through Gaussian measurements.
Specifically, while the quantum contribution may be important at low
temperatures, in the high temperature limit the entropy production corresponds
to purely classical position-momentum correlations. Our results demonstrate an
important difference between fermionic and bosonic systems regarding the
existence of a quantum-to-classical transition in the microscopic formulation
of the entropy production. They also show that entropy production can be mainly
caused by quantum correlations even in the weak coupling limit, which admits a
description in terms of classical rate equations for state populations, as well
as in the low particle density limit, where the transport properties of both
bosons and fermions converge to those of classical particles.
