Related papers: Geometric conservation in curved spacetime and ent…
A generalized entropy arising in the context of superstatistics is obtained for an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric…
A conserved current for generic quadratic curvature gravitational models is defined, and it is shown that, at the linearized level, it corresponds to the Deser-Tekin charges. An explicit expression for the charge for new massive gravity in…
Recently we showed that in FLRW cosmology, the contribution from higher curvature terms in any generic metric gravity theory to the energy-momentum tensor is of the perfect fluid form. Such a geometric perfect fluid can be interpreted as a…
We analyze the equilibrium space of an ideal gas using the formalism of geometrothermodynamics. We introduce the concept of thermodynamic geodesics to show that the equilibrium space around a particular initial state can be divided into two…
We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a…
In hydrodynamics the existence of an entropy current with non-negative divergence is related to the existence of a time-independent solution in a static background. Recently there has been a proposal for how to construct an entropy current…
n scalar-tensor theories of gravity with torsion, the gravitational field is described in terms of a symmetric metric tensor $g$, a metric-compatible connection $\nabla$ with torsion, and a scalar field $\phi$. The main aim is to explore an…
The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on…
We investigate properties of the conserved charge in general relativity, recently proposed by one of the present authors with his collaborators, in the inflation era, the matter dominated era and the radiation dominated era of the expanding…
We construct an entropy current using a supersymmetric formulation of the low-energy effective action for the Schwinger-Keldysh generating functional. We define an entropy current quantum mechanically by coupling it to an external source.…
In any generally covariant theory of gravity, we show the relationship between the linearized asymptotically conserved current and its non-linear completion through the identically conserved current. Our formulation for conserved charges is…
From the constructions of the quantum spacetime, a four dimensional quantized spacetime can be embedded in a five dimensional continuous spacetime. Thus to observe from the five dimensional continuous spacetime where the four dimensional…
Provided a quantum superconducting condensate is allowed to occupy a curved hyper-plane of space-time, a geometric potential from the kinetic term arises. An energy conservation relation involving the geometric field at every material point…
It is pointed out that in curved spacetime, one cannot define the sum of energy-momemtum 4-vector over a space-like hypersurface. The difficulty in finding satisfactory gravitational energy-momentum complex stems from misunderstanding of…
We provide a general formulation for calculating conserved charges for solutions to generally covariant gravitational theories with possibly other internal gauge symmetries, in any dimensions and with generic asymptotic behaviors. These…
Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in $n>1$ dimensions. Apart from entropy, which is a well-know invariant, three additional invariants are found from an…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
We identify a conserved quantity in continuous-time optimization dynamics, termed computational inertia. Defined as the sum of kinetic energy (parameter velocity) and potential energy (loss), this scalar remains invariant under idealized,…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption…