The Statistical Foundations of Entropy
In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory...
Gespeichert in:
| Format: | Online |
|---|---|
| Sprache: | Englisch |
| Veröffentlicht: |
MDPI - Multidisciplinary Digital Publishing Institute
2022
|
| Schlagworte: | |
| Online-Zugang: | ONIX_20220506_9783036535579_23 |
| Tags: |
Keine Tags, Fügen Sie das erste Tag hinzu!
|
| _version_ | 1863744550428737536 |
|---|---|
| collection | Directory of Open Access Books |
| description | In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann–Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann–Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems. |
| format | Online |
| id | doab-20.500.12854ir-80958 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-809582024-03-28T03:32:28Z The Statistical Foundations of Entropy Jizba, Petr Korbel, Jan ecological inference generalized cross entropy distributional weighted regression matrix adjustment entropy critical phenomena renormalization multiscale thermodynamics GENERIC non-Newtonian calculus non-Diophantine arithmetic Kolmogorov–Nagumo averages escort probabilities generalized entropies maximum entropy principle MaxEnt distribution calibration invariance Lagrange multipliers generalized Bilal distribution adaptive Type-II progressive hybrid censoring scheme maximum likelihood estimation Bayesian estimation Lindley’s approximation confidence interval Markov chain Monte Carlo method Rényi entropy Tsallis entropy entropic uncertainty relations quantum metrology non-equilibrium thermodynamics variational entropy rényi entropy tsallis entropy landsberg—vedral entropy gaussian entropy sharma—mittal entropy α-mutual information α-channel capacity maximum entropy Bayesian inference updating probabilities n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann–Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann–Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems. 2022-05-06T11:18:12Z 2022-05-06T11:18:12Z 2022 book ONIX_20220506_9783036535579_23 9783036535579 9783036535586 https://directory.doabooks.org/handle/20.500.12854/80958 eng image/jpeg Attribution 4.0 International https://mdpi.com/books/pdfview/book/5297 https://mdpi.com/books/pdfview/book/5297 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-3558-6 10.3390/books978-3-0365-3558-6 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036535579 9783036535586 182 Basel open access |
| spellingShingle | ecological inference generalized cross entropy distributional weighted regression matrix adjustment entropy critical phenomena renormalization multiscale thermodynamics GENERIC non-Newtonian calculus non-Diophantine arithmetic Kolmogorov–Nagumo averages escort probabilities generalized entropies maximum entropy principle MaxEnt distribution calibration invariance Lagrange multipliers generalized Bilal distribution adaptive Type-II progressive hybrid censoring scheme maximum likelihood estimation Bayesian estimation Lindley’s approximation confidence interval Markov chain Monte Carlo method Rényi entropy Tsallis entropy entropic uncertainty relations quantum metrology non-equilibrium thermodynamics variational entropy rényi entropy tsallis entropy landsberg—vedral entropy gaussian entropy sharma—mittal entropy α-mutual information α-channel capacity maximum entropy Bayesian inference updating probabilities n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science The Statistical Foundations of Entropy |
| title | The Statistical Foundations of Entropy |
| title_full | The Statistical Foundations of Entropy |
| title_fullStr | The Statistical Foundations of Entropy |
| title_full_unstemmed | The Statistical Foundations of Entropy |
| title_short | The Statistical Foundations of Entropy |
| title_sort | statistical foundations of entropy |
| topic | ecological inference generalized cross entropy distributional weighted regression matrix adjustment entropy critical phenomena renormalization multiscale thermodynamics GENERIC non-Newtonian calculus non-Diophantine arithmetic Kolmogorov–Nagumo averages escort probabilities generalized entropies maximum entropy principle MaxEnt distribution calibration invariance Lagrange multipliers generalized Bilal distribution adaptive Type-II progressive hybrid censoring scheme maximum likelihood estimation Bayesian estimation Lindley’s approximation confidence interval Markov chain Monte Carlo method Rényi entropy Tsallis entropy entropic uncertainty relations quantum metrology non-equilibrium thermodynamics variational entropy rényi entropy tsallis entropy landsberg—vedral entropy gaussian entropy sharma—mittal entropy α-mutual information α-channel capacity maximum entropy Bayesian inference updating probabilities n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | ecological inference generalized cross entropy distributional weighted regression matrix adjustment entropy critical phenomena renormalization multiscale thermodynamics GENERIC non-Newtonian calculus non-Diophantine arithmetic Kolmogorov–Nagumo averages escort probabilities generalized entropies maximum entropy principle MaxEnt distribution calibration invariance Lagrange multipliers generalized Bilal distribution adaptive Type-II progressive hybrid censoring scheme maximum likelihood estimation Bayesian estimation Lindley’s approximation confidence interval Markov chain Monte Carlo method Rényi entropy Tsallis entropy entropic uncertainty relations quantum metrology non-equilibrium thermodynamics variational entropy rényi entropy tsallis entropy landsberg—vedral entropy gaussian entropy sharma—mittal entropy α-mutual information α-channel capacity maximum entropy Bayesian inference updating probabilities n/a thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20220506_9783036535579_23 |