  We provide an improved definition of new conserved quantities derived from
the energy-momentum tensor in curved spacetime by introducing an additional
scalar function. We find that the conserved current and the associated
conserved charge become geometric under a certain initial condition of the
scalar function, and show that such a conserved geometric current generally
exists in curved spacetime. Furthermore, we demonstrate that the geometric
conserved current agrees with the entropy current for the perfect fluid, thus
the conserved charge is the total entropy of the system. While the geometric
charge can be regarded as the entropy for non-dissipative fluid, its physical
meaning should be investigated for more general cases.
