  We investigate an unconventional nature of the entropy production (EP) in
nonequilibrium systems with odd-parity variables that change signs under time
reversal. We consider the Brownian motion of a particle in contact with a heat
reservoir, where particle momentum is an odd-parity variable. In the presence
of an {\it external} momentum-dependent force, the EP transferred to
environment is found {\em not} equivalent to usual reservoir entropy change due
to heat transfer. There appears an additional unconventional contribution to
the EP, which is crucial for maintaining the non-negativity of the (average)
total EP enforced by the thermodynamic second law. A few examples are
considered to elucidate the novel nature of the EP. We also discuss detailed
balance conditions with a momentum-dependent force.
