  We propose a new class of vector fields to construct a conserved charge in a
general field theory whose energy momentum tensor is covariantly conserved. We
show that there always exists such a vector field in a given field theory even
without global symmetry. We also argue that the conserved current constructed
from the (asymptotically) time-like vector field can be identified with the
entropy current of the system. As a piece of evidence we show that the
conserved charge defined therefrom satisfies the first law of thermodynamics
for an isotropic system with a suitable definition of temperature. We apply our
formulation to several gravitational systems such as the expanding universe,
Schwarzschild and BTZ black holes, and gravitational plane waves. We confirm
the conservation of the proposed entropy density under any homogeneous and
isotropic expansion of the universe, the precise reproduction of the
Bekenstein-Hawking entropy incorporating the first law of thermodynamics, and
the existence of gravitational plane wave carrying no charge, respectively. We
also comment on the energy conservation during gravitational collapse in simple
models.
