Probability and Entropy in Quantum Theory

Caticha, Ariel

doi:10.1007/978-94-011-4710-1_25

Cited by 11 publications

(10 citation statements)

References 28 publications

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“…On the basis of this choice of prior one can derive a considerable amount of the formalism of quantum mechanics. This includes the "postulates" that quantum states form a Hilbert space, that probabilities are computed through the Born rule, and that time evolution is unitary [17].…”

Section: Introductionmentioning

confidence: 99%

Maximum entropy, fluctuations and priors

Caticha

2001

AIP Conference Proceedings

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The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to be ruled out. Two applications are given. The first is to the theory of thermodynamic fluctuations. The formulation is exact, covariant under changes of coordinates, and allows fluctuations of both the extensive and the conjugate intensive variables. The second application is to the construction of an objective prior for Bayesian inference. The prior obtained by following the ME method to its inevitable conclusion turns out to be a special case (α = 1) of what are currently known under the name of entropic priors.

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Section: Introductionmentioning

confidence: 99%

Maximum entropy, fluctuations and priors

Caticha

2001

AIP Conference Proceedings

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“…In the "Pure States", there are conditions where the von Neumann entropy is equal to the Shannon entropy (Bennett & Shor, 1998). Caticha (1998) argues that although probabilities play a most central role in quantum mechanics, the concept of entropy appears only later as an auxiliary quantity to be used only when a problem is sufficiently complicated that "clean" deductive methods have failed and indicates the relationships between the von Neumann and Shannon entropies with respect to the quantum entropy. Meier (1962), in his book "A Communications Theory of Urban Growth", has attempted to build a systematic theory of urban growth based on the concept of information flows, inspired from Shannon's information theory and its related concepts such as "Channel", "Channel Capacity", "Sender" and "Receiver".…”

Section: Iii8 Quantum Information Theorymentioning

confidence: 99%

City and Regional Planning

Gribb¹

2012

21st Century Geography: A Reference Handbook

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“…This is clearly valuable in circumstances where microscopic dynamics may be too far removed from the phenomena of interest, such as in complex biological or ecological systems, or where it may be unknown or perhaps even nonexistent, as in economics. It has already been shown that entropic arguments do account for a substantial part of the formalism of quantum mechanics, a theory that is presumably fundamental [18]. Perhaps the fundamental theories of physics are not so fundamental; they may just be consistent, objective ways of manipulating information.…”

Section: Introductionmentioning

confidence: 99%

Complexity characterization in a probabilistic approach to dynamical systems through information geometry and inductive inference

et al. 2012

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Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we investigate the possibility of describing the macroscopic behavior of complex systems in terms of the underlying statistical structure of their microscopic degrees of freedom by use of statistical inductive inference and information geometry. We review the Maximum Relative Entropy (MrE) formalism and the theoretical structure of the information geometrodynamical approach to chaos (IGAC) on statistical manifolds MS. Special focus is devoted to the description of the roles played by the sectional curvature KM S , the Jacobi field intensity JM S and the information geometrodynamical entropy SM S (IGE). These quantities serve as powerful information geometric complexity measures of information-constrained dynamics associated with arbitrary chaotic and regular systems defined on MS. Finally, the application of such information geometric techniques to several theoretical models are presented.

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Probability and Entropy in Quantum Theory

Abstract: Entropic arguments are shown to play a central role in the foundations of quantum theory. We prove that probabilities are given by the modulus squared of wave functions, and that the time evolution of states is linear and also unitary.

Cited by 11 publications

References 28 publications

Maximum entropy, fluctuations and priors

Maximum entropy, fluctuations and priors

City and Regional Planning

Complexity characterization in a probabilistic approach to dynamical systems through information geometry and inductive inference

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