The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respectively. For Einstein’s GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived from this Noether current although it definitely vanishes. ...

Assigning the variations of internal energy into heat or work contributions is a challenging task due to fact that these properties are trajectory dependent. A number proposals have been put forward for open quantum systems following an arbitrary dynamics. We here focus on nonequilibrium thermodynamics two-level system and explore in addition conventional approach, two definitions motivated by ...

A bstract We present a modified implementation of the Euclidean action formalism suitable for studying thermodynamics class cosmological solutions containing Killing horizons. To obtain real metric definite signature, we perform “triple Wick-rotation” by analytically continuing all spacelike directions. The resulting geometry is used to calculate on-shell action, which defines thermodynamic pot...

Fluctuations of the excess heat in an out of equilibrium steady state are experimentally investigated in two stochastic systems : an electric circuit with an imposed mean current and a harmonic oscillator driven out of equilibrium by a periodic torque. In these two linear systems, we study excess heat that represents the difference between the dissipated heat out of equilibrium and the dissipat...