Related papers: Noether's theorem applied to GENERIC
We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…
We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether…
In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole…
We present and discuss the two-generator framework of nonequilibrium thermodynamics known as GENERIC ("general equation for the nonequilibrium reversible-irreversible coupling"), which is based on geometric concepts and on statistical…
We clarify the relation between the Noether charge associated to an arbitrary vector field and the equations of motions by revisiting Wald formalism. For a time-like Killing vector, aspects of the Noether charge suggest that it is dual to…
This paper contains a fully geometric formulation of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the sum of Hamiltonian mechanics and gradient dynamics, is a framework…
We study the thermodynamic entropy as a Noether invariant in a stochastic process. Following the Onsager theory, we consider the Langevin equation for a thermodynamic variable in a thermally isolated system. By analyzing the…
We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both…
When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…
Two techniques for computing black hole entropy in generally covariant gravity theories including arbitrary higher derivative interactions are studied. The techniques are Wald's Noether charge approach introduced recently, and a field…
We consider two non-statistical definitions of entropy for dynamic (non-stationary) black holes in spherical symmetry. The first is analogous to the original Clausius definition of thermodynamic entropy: there is a first law containing an…
I study the balance law equation of surface charges in the presence of background fields. The construction allows a unified description of Noether's theorem for both global and local symmetries. From the balance law associated with some of…
In any diffeomorphism invariant theory of gravity, one can define a Noether charge arising from the invariance of the Lagrangian under diffeomorphisms. We have determined the Noether charge for scalar-tensor theories of gravity, in which…
The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether Charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole…
Noether's theorem is reviewed with a particular focus on an intermediate step between global and local gauge and coordinate transformations, namely linear transformations. We rederive the well known result that global symmetry leads to…
This paper provides a modern presentation of Noether's theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close…
We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with…
We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation $\delta Q = T \delta S$. Our proof relies on extending previous arguments by using a more general definition of the Noether…
In Noether's original presentation of her celebrated theorm of 1918 allowance was made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon…
Recently Hollands, Wald and Zhang proposed a new formula for the entropy of a dynamical black hole for an arbitrary theory of gravity obtained from a diffeomorphism covariant Lagrangian via the Noether charge method. We present an…