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# Entropy in thermodynamics and information theory

About: Entropy in thermodynamics and information theory is a research topic. Over the lifetime, 1119 publications have been published within this topic receiving 44301 citations.

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TL;DR: In this paper, a generalized form of entropy was proposed for the Boltzmann-Gibbs statistics with the q→1 limit, and the main properties associated with this entropy were established, particularly those corresponding to the microcanonical and canonical ensembles.

Abstract: With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS
q
≡k [1 – ∑
i=1
W
p
i
q
]/(q-1), whereq∈ℝ characterizes the generalization andp
i are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.

8,239 citations

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TL;DR: In this paper, the concept of black-hole entropy was introduced as a measure of information about a black hole interior which is inaccessible to an exterior observer, and it was shown that the entropy is equal to the ratio of the black hole area to the square of the Planck length times a dimensionless constant of order unity.

Abstract: There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.

6,591 citations

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TL;DR: In this article, the authors considered the problem of computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation, and showed that the entropy of this density matrix is given by the area of a minimal surface.

Abstract: We consider classical Euclidean gravity solutions with a boundary. The bound- ary contains a non-contractible circle. These solutions can be interpreted as computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation. When the circle is contractible in the bulk, we argue that the entropy of this density matrix is given by the area of a minimal surface. This is a generalization of the usual black hole entropy formula to euclidean solutions without a Killing vector. A particular example of this set up appears in the computation of the entanglement entropy of a subregion of a field theory with a gravity dual. In this context, the minimal area prescription was proposed by Ryu and Takayanagi. Our arguments explain their conjecture.

1,332 citations

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01 Jan 1993

TL;DR: In this article, the authors introduce fundamental concepts for Entropies for Finite Quantum Systems and postulates for Entropy and Relative Entropy for General Quantum Systems, as well as Modular Theory and Auxiliaries.

Abstract: I Entropies for Finite Quantum Systems.- 1 Fundamental Concepts.- 2 Postulates for Entropy and Relative Entropy.- 3 Convex Trace Functions.- II Entropies for General Quantum Systems.- 4 Modular Theory and Auxiliaries.- 5 Relative Entropy of States of Operator Algebras.- 6 From Relative Entropy to Entropy.- 7 Functionals of Entropy Type.- III Channeling Transformation and Coarse Graining.- 8 Channels and Their Transpose.- 9 Sufficient Channels and Measurements.- 10 Dynamical Entropy.- 11 Stationary Processes.- IV Perturbation Theory.- 12 Perturbation of States.- 13 Variational Expression of Perturbational Limits.- V Miscellanea.- 14 Central Limit and Quasi-free Reduction.- 15 Thermodynamics of Quantum Spin Systems.- 16 Entropic Uncertainty Relations.- 17 Temperley-Lieb Algebras and Index.- 18 Optical Communication Processes.

1,228 citations

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01 Jan 1992

TL;DR: Applications of Jaynes' maximum entropy principle and Kullback's minimum cross-entropy principle are applied to develop new entropy optimization principles generalized principles of maximum entropy the four inverse maximum entropy principles.

Abstract: Entropy optimization principles Jaynes' maximum entropy principle applications of Jaynes' maximum entropy principle Kullback's minimum cross-entropy principle further applications of MaxEnt and MinEnt new entropy optimization principles generalized principles of maximum entropy the four inverse maximum entropy principles.

1,050 citations