Related papers: Dimensional Equations of Entropy
The definition of entropy obtained for stationary black holes is extended in this paper to the case of non-stationary black holes. Entropy is defined as a macroscopical thermodynamical quantity which satisfies the first principle of…
A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…
Bekenstein's inequality sets a bound on the entropy of a charged macroscopic body. Such a bound is understood as a universal relation between physical quantities and fundamental constants of nature that should be valid for any physical…
After a discussion on several limiting cases where General Relativity turns into less sophisticated theories, we find that in the correct thermodynamical and cosmological weak field limit of Einstein's field equations the entropy of the…
Entropy, since its first discovery by Ludwig Boltzmann in 1877, has been widely applied in diverse disciplines, including thermodynamics, continuum mechanics, mathematical analysis, machine learning, etc. In this paper, we propose a new…
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…
The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This…
The unification of gravity with the three other forces has been an important goal of physics for some time now, because a quantum theory of gravity is necessary to explain the universe at its earliest moments. Its pursuit has largely…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
Diffusivity, a measure for how rapidly a fluid self-mixes, shows an intimate, but seemingly fragmented, connection to thermodynamics. On one hand, the "configurational" contribution to entropy (related to the number of mechanically-stable…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all…
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the…
Shannon's entropy and other entropy-based concepts are derived from the new, more general concept of relative divergence of one "grading' function on a linearly ordered set from another such function. The definition of relative divergence…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…
The entropy of classical thermodynamics is uniquely determined by the relation of adiabatical accessibilty between equilibrium states of thermodynamical systems. This review outlines the logical path leading to this results and the…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…
Two major apparently unrelated problems, that of the origin of time in the universe associated with quantum gravity and to the entropy in de Sitter cosmological models, are found to have their origin in a single physical phenomenon: the…