Recently, it has been shown that for a dynamical black hole in any higher derivative theory of gravity, one could construct a spatial entropy current, characterizing the in/outflow of entropy at every point on the horizon, as long as the dynamics of the amplitude is small enough. However, the construction is very much dependent on how we choose the spatial slicing of the horizon along its null generators. In this note, we have shown that though both the entropy density and the spatial entropy current change nontrivially under a reparametrization of the null generator, the net entropy production, which is given by the 'time' derivative of entropy density plus the divergence of the spatial current is invariant. We have explicitly verified this claim for the particular case of dynamical black holes Einstein-Gauss-Bonnet theory.1 We are deeply saddened to lose our friend and collaborator, Pooja Jethwani. She was an active collaborator in this project and had seen its completion before the end of our time together.

The main objective of this work is to study the mixed state version of the Jaynes-Cummings model in the context of two-level atom interacting with a mixed field state of a squeezed vacuum and a coherent state. Here, the pure squeezed coherent state (PSCS) and the mixed squeezed coherent state (MSCS) have been used as the states of the radiation field. The photon-counting distribution (PCD), the atomic inversion and the entanglement dynamics of atom-field interaction for both the radiation fields are investigated and compared with each other. We observe that depending on the state of the field, squeezing has very different effects on coherent photons. Mild squeezing on the coherent photons localizes the PCD for PSCS; however, for MSCS there is no such localization observed -instead squeezing manifests for MSCS as oscillations in the PCD. The effects of squeezing on the atomic inversion and the entanglement dynamics for PSCS are very different as compared with the corresponding quantities associated with MSCS; in fact, they are contrasting. It is well known in the literature that for PSCS, increasing the squeezing increases the well-known ringing revivals in the atomic inversion, and also increases irregularity in the entanglement dynamics. However, increasing the squeezing in MSCS very significantly alters the collapse-revival pattern in the atomic inversion and the entanglement dynamics of the Jaynes-Cummings model. For MSCS, the effect of squeezing on the quadrature variables and Mandel's Q parameter are also presented.