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The present work reveals a direct correspondence between modified theories of gravity (cosmology) and entropic cosmology based on the thermodynamics of apparent horizon. It turns out that due to the total differentiable property of entropy,…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
In his ninth memoir Clausius summarizes the two principles of thermodynamics as follows: "The whole mechanical theory of heat rests on two fundamental theorems: that of equivalence of heat and work, and that of equivalence of…
In this paper, we obtain the law of emergence with Tsallis entropy from the thermodynamic laws. We first derive the law of emergence from the equilibrium description of the unified first law and Clausius relation. However, it has been shown…
Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. In this letter, we begin the study of this new formula to obtain the first law of thermodynamics for dynamical…
It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be…
Spacetimes with horizons show a resemblance to thermodynamic systems and it is possible to associate the notions of temperature and entropy with them. Several aspects of this connection are reviewed in a manner appropriate for broad…
We propose a modified gravity theory by extending the Einstein-Hilbert action with an arbitrary function of the Ricci scalar and the Kretschmann scalar invariants. The resulting modified Friedmann equations for a spatially flat FRW universe…
The equivalence principle and its universality enables the geometrical formulation of gravity. In the standard formulation of General Relativity \'a la Einstein, the gravitational interaction is geometrized in terms of the spacetime…
A scalar field in the ground state, when partially hidden from observation by a spherical boundary, acquires entanglement entropy $S$ proportional to the area of the surface. This area law is well established in flat space, where it follows…
The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…
Recently, Chandrasekaran, Penington and Witten (CPW) have shown that the generalized entropy of the Schwarzschild black hole at the bifurcation surface equals the entropy of an extended von Neumann algebra of quantum observables in the…
Verlinde has recently conjectured, via a Beckenstein-like thought experiment, that gravitation, instead of being an elementary force, is an emergent entropic one. This rather surprising conjecture was actually proved in [Physica A {\bf 505}…
It has been recently shown that the Bekenstein entropy bound is not respected by the systems satisfying modified forms of Heisenberg uncertainty principle (HUP) including the generalized and extended uncertainty principles, or even their…
The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of $\phi ^{4}$ theory as a mean value between states and observables defined through the correlation functions.…
This study investigates the implications of adopting fractional entropy in the area law framework and demonstrates its natural alignment with an isothermal description of black hole composition. We discuss the Zeroth law compatibility of…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In…
When the difference between changes in energy and entropy at a given temperature is correlated with the ratio between the same changes in energy and entropy at zero average free energy of an ensemble of similar but distinct molecule-sized…