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…lude the formation of typical crystals, the workings of a [[refrigerator]] and living organisms, used in thermodynamics. …include the formation of typical crystals, the workings of a refrigerator and living organisms, used in thermodynamics.

{{Information theory}} …atistics]], the '''Kullback–Leibler divergence''' (also called '''relative entropy''') is a measure of how one [[probability distribution]] is different from

已由[[用户:Yillia Jing]]进行初步翻译，已由[[用户:Flipped]]进行审校。{{Information theory}} …th>H(Y|X)</math>。两个圆中间的交集部分（紫色的部分）表示二者的<font color="#ff8000">'''互信息 Mutual information，（MI）'''</font><math>\operatorname{I}(X;Y)</math>）。]]

…established edifice. This article will try to sketch some approaches to it and some concepts important for it. …established edifice. This article will try to sketch some approaches to it and some concepts important for it.

…is at the heart of the [[principle of locality|disparity between classical and quantum physics]]: entanglement is a primary feature of quantum mechanics… …of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics lac

{{short description|Hungarian-American mathematician and physicist (1903–1957)}} | death_date = {{death date and age|mf=yes|1957|2|8|1903|12|28}}

…cite book|first=Roberto|last=Ligrone|date=2019|chapter=Glossary|department=Entropy|chapter-url=https://books.google.ca/books?id=c86aDwAAQBAJ&pg=PA478|title=Bi

…vide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from [[classical mechanics]] (in particular,… …vide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most

The first and third values are exact; the second is exactly equal to {{sfrac|1380649|1602 The first and third values are exact; the second is exactly equal to . See the linked sec

…ty principle, 1927.jpg|thumb|Canonical commutation rule for position ''q'' and momentum ''p'' variables of a particle, 1927. ''pq'' − ''qp'' = ''h''/2'' …antities of a [[particle]], such as [[Position (vector)|position]], ''x'', and [[momentum]], ''p'', can be predicted from [[initial condition]]s.

| pdf_caption = The red curve is the ''standard normal distribution'' | pdf_caption = The red curve is the standard normal distribution

…y of Communication]]" in the ''[[Bell System Technical Journal]]'' in July and October 1948. …ical Theory of Communication" in the Bell System Technical Journal in July and October 1948.

…ty%20of%20natural%20processes%20and%20the%20asymmetry%20between%20future%20and%20past.%22 111]}}</ref> …. 79–107.</ref><ref>Bailyn, M. (1994), Section 71, pp. 113–154.</ref> '''熵 Entropy'''来解释。若一个'''孤立系统 Isolated System'''最初在具有隔

…thers. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macros …thers. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopi

{{for|the novel|Random Walk}} …ion|Mathematical formalization of a path that consists of a succession of random steps}}

…Casas-Vázquez 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers'', === Difference between equilibrium and non-equilibrium thermodynamics 平衡与非平衡热力学之间的差异 =

…um stationary state | url = | journal = Journal of Physics A: Mathematical and Theoretical | volume = 40 | issue = 3| pages = 371–380 | doi=10.1088/1751

…disambiguation)]]. For "Life" in the personal sense, see [[Personal life]] and [[Everyday life]].}} {{pp-semi-vandalism|small=yes}}

'''信息论 Information theory'''研究的是信息的量化、存储与传播。信息论最初是 …eb.archive.org/web/20110723045720/http://aicanderson2.home.comcast.net/~aicanderson2/home.pdf|archivedate=July 23, 2011|url-status=dead|accessdate=2010-06

{{thermodynamics|cTopic=History and Culture}} …so, albeit in a subtle manner, motivated new directions in [[probability]] and [[statistics]]; see, for example, the [[timeline of thermodynamics]].

…tions of a Resilience Framework | journal = [[Annual Review of Environment and Resources]] | volume = 32 | pages = 395–419 | doi=10.1146/annurev.energy. …rnal stresses imposed upon it by climate change and (2) adapt, reorganize, and evolve into more desirable configurations that improve the sustainability…

…gy|total energy]], [[Thermodynamic free energy|free energy]], [[entropy]], and [[pressure]], can be expressed in terms of the partition function or its [[ …any physical meanings, as discussed in [[#Meaning and significance|Meaning and significance]].

…en |first4=Juho |last5=Gabbouj |first5=Moncef |last6=Iosifidis |first6=Alexandros |date=July 2017 |title=Forecasting Stock Prices from the Limit Order Boo …al image analysis, natural language processing, brain–computer interfaces, and financial time series.

== Fitness Landscape Epistasis And Recombination == By MANUEL BELTRÁN DEL RÍO, CHRISTOPHER R. STEPHENS, and DAVID A. ROSENBLUETH<br>

…熵是指在给定过去值Y得到过去值X时，Y值不确定性的减少量。更具体地，如果Xt和Yt（t∈N）表示两个随机过程，且信息量用'''香农熵 Shannon entropy'''测量，则转移熵可以写为： …fer between financial time series|journal=Physica A: Statistical Mechanics and Its Applications|language=en|volume=391|issue=10|pages=2971–2989|doi=10.1

== Fisher transfer entropy: quantifying the gain in transient sensitivity == …a ferromagnetic two-dimensional lattice Ising model with Glauber dynamics and is shown to diverge at the critical point.''

…Casas-Vázquez 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers'',

== Scaling and universality in urban economic diversification == …c implications of open-ended diversity created by urbanization, for understanding the observed empirical distribution. Given the universal distribution,…

By Aldo Mascareño, Eric Goles, and Gonzalo A. Ruz …crises, their temporal transitions (incubation, contagion, restructuring), and the suitable modeling techniques to represent them. Third, we illustrate th

…koszka|first1=Andrzej|title=States of Consciousness: Models for Psychology and Psychotherapy|date=2007|publisher=Springer Science & Business Media|locatio

…'、'''<font color="#ff8000"> 能量 energy</font>'''和'''<font color="#ff8000">熵 entropy</font>'''，这些物理量表征处于热力学平衡的热力学系统。 …ef name="LJCV 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'',

…irst2=Joy A.|last1=Cover|last2=Thomas|isbn=0-471-06259-6|title=Elements of Information Theory|year=1991|publisher=Wiley|location=New York|url=https://archive.org/

{{Information theory}} …1948 and was based in part on earlier work and ideas of [[Harry Nyquist]] and [[Ralph Hartley]].

…dynamic equilibrium]] in an environment with which it exchanges [[energy]] and [[matter]]. A tornado may be thought of as a dissipative system. …common examples include [[laser]]s, [[Bénard cells]], [[droplet cluster]], and the [[Belousov–Zhabotinsky reaction]].<ref name=":0">{{cite journal|last1

…non-life, whereas consciousness is spontaneously generated from life. Life and consciousness appear to have strikingly comparable self-generating systems. …-line researchers in areas including physics,biology,philosophy of science and computer science.They organized this three-season "Self-Generating Structur

{{short description|The multiple interactions and regulation of life forms with their environment}} …re maintained by flowing [[information]], [[energy flow (ecology)|energy]] and [[matter]].

…the nineteenth century, evolutive abiogenesis means increasing complexity and evolution of matter from inert to living state in the abiotic context of ev …5 |title= A New History of Life: the radical discoveries about the origins and evolution of life on earth |publisher= Bloomsbury Press |pages= 39–40 |is

…t|Maximum Power Principle in [[Energy Systems Language]] adapted from Odum and Odum 2000, p. 38|链接=Special:FilePath/MaximumPowerESL.gif]] …er intake, energy transformation, and those uses that reinforce production and efficiency."<ref>H.T. Odum 1995, p.&nbsp;311</ref>

{{Short description|Situations involving imperfect or unknown information}} …logy]], [[engineering]], [[metrology]], [[meteorology]], [[ecology]] and [[information science]].

…ref><ref name=":1">Hoel E P. When the map is better than the territory[J]. Entropy, 2017, 19(5): 188.</ref>。马尔可夫动力学系统是指系统在某一 …生物学家[[Erik hoel|Erik Hoel]]尝试将因果引入涌现的衡量，提出了因果涌现这一概念，并且使用[[有效信息]]（Effective Information，简称EI）来量化系统动力学的因果性强弱<ref name=":0" /><re

…ig, H.: (2009) "Exact thermodynamic principles for dynamic order existence and evolution in chaos", ''Chaos, Solitons & Fractals'', v. '''41(4)''', pp. 19

…Berdahl, Christa Brelsford, Caterina De Bacco, Marion Dumas, Vanessa Ferdinand, Joshua A. Grochow, Laurent Hébert-Dufresne, Yoav Kallus, Christopher P. K …which can be facilitated in biological systems by horizontal transmission and in social systems by active spreading strategies of infected individuals.''

…d 13 (aqua). Such arrangements have been noticed since the [[Middle Ages]] and can be used to make mathematical models of a wide variety of plants.]] …s: Cells and their physical constraints | journal = Progress in Biophysics and Molecular Biology | volume = 122 | issue = 1 | pages = 58–69 | date = Oct

…= Ludwig | title = The second law of thermodynamics (Theoretical physics and philosophical problems)| publisher = Springer-Verlag New York, LLC | year… …s.google.com/books?id=96AAAAAAMAAJ|location=New York|publisher=D. Van Nostrand|year=1876}}</ref></blockquote>

…L }}</ref> Recurrent neural networks are theoretically [[Turing complete]] and can run arbitrary programs to process arbitrary sequences of inputs.<ref>{{ …h recognition. Recurrent neural networks are theoretically Turing complete and can run arbitrary programs to process arbitrary sequences of inputs.

作者：Espinosa, Angela and Walker, Jon [[合作物种：人类的互惠性及演化 A Cooperative Species: Human Reciprocity and Its Evolution]]（未建立词条）

…e of three basic machine learning paradigms, alongside supervised learning and unsupervised learning. …e of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.

…e activities can be viewed as two facets of the same field of application, and together they have undergone substantial development over the past few deca …e activities can be viewed as two facets of the same field of application, and together they have undergone substantial development over the past few deca

…computer scientist) |author=Charles H. Bennett |journal=Studies in History and Philosophy of Modern Physics |volume=34 |issue=3 |pages=501–510 |year=200 …//spectrum.ieee.org/computing/hardware/landauer-limit-demonstrated |title=Landauer Limit Demonstrated - IEEE Spectrum |publisher=Spectrum.ieee.org |date=

…>{{Citation|journal=Evolutionary Systems| title=Selected self-organization and the semiotics of evolutionary systems| year=1998| first=Luis M.| last=Rocha …f the DNA molecule by Watson and Crick and how it is separately translated and replicated in the cell.

* 1. Complexity, Entropy and the Physics of Information …件:Complexity,entropy and.jpg|居中|缩略图|Complexity, Entropy and the Physics of Information]]

| publisher = Longmans， Green and Co. …e=Slovenian |trans-title=Ludwig Boltzmann and the First Student of Physics and Mathematics of Slovene Descent |date=December 2001 |last=Južnič |first=St

Again and again, the impossible problem is solved when we see that the problem is onl Again and again, the impossible problem is solved when we see that the problem is onl

…ing [[science]], [[engineering]], [[philosophy]], [[medicine]], [[sport]], and [[law]]. In the philosophy of [[decision theory]], Bayesian inference is cl …are compatible with rationality, according to philosophers [[Ian Hacking]] and [[Bas van&nbsp;Fraassen]].<ref>Stanford encyclopedia of philosophy; Bayesia

…f>{{cite book |last = Waldner|first = Jean-Baptiste |title = Nanocomputers and Swarm Intelligence |publisher = ISTE Ltd John Wiley & Sons|place = London… …通信方法常被作为一种典型范式<ref>{{cite book |last = Monmarché Nicolas, Guinand Frédéric and Siarry Patrick |title = Artificial Ants |publisher = Wiley-ISTE |year =…

…ms assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concern …nitial state. Stronger properties, such as [[mixing (mathematics)|mixing]] and [[equidistribution]], have also been extensively studied.

…oi=10.4204/EPTCS.95.1|issn=2075-2180|arxiv=1111.3620|s2cid=9046880}}</ref> and [[Coupling (probability)|probabilistic couplings]].<ref name=":11">{{Cite… …ne|first=Arthur|date=1982-02-01|title=Hidden Variables, Joint Probability, and the Bell Inequalities|journal=Physical Review Letters|volume=48|issue=5|pag

…cell has not yet been achieved in a laboratory setting, the goal to understand the process appears well within reach.<ref name="Exploring">{{cite web |url | first2 = Alexander

{{Short description|Model for generating observable data in probability and statistics}} …rvnb|Jebara|2004}}, and {{harvnb|Mitchell|2015}}, give different divisions and definitions.}} but three major types can be distinguished, following {{harv

…aft is better looking than Limestone, but Limestone projects seaworthiness and reliability）。（两种态度，两个品牌）。 …量化模式提供了线索，即根据对一个人的语言行为的分析来研究其心理状态。<ref name=":4">Gottschalk, Louis August, and Goldine C. Gleser. The measurement of psychological states through the cont

…12page2922">{{cite book|author=J. Michael Steele|title=Stochastic Calculus and Financial Applications|url=https://books.google.com/books?id=fsgkBAAAQBAJ&p …eele200122">{{cite book|author=J. Michael Steele|title=Stochastic Calculus and Financial Applications|url=https://books.google.com/books?id=H06xzeRQgV4C|y

在关于'''游荡集合 Wandering Sets'''的文章中给出了一种对耗散系统进行数学建模的 …phase transition between maximum entropy production structures and minimum entropy production structures?|journal=Complexity|date=2 January 2015|volume=20|iss

…ion: Transactions of the University of Illinois Symposium, H. Von Foerster and G. W. Zopf, Jr. (eds.), Pergamon Press: London, UK, pp. 255–278.</ref>它 …date=2018|title=Of woodlice and men: A Bayesian account of cognition, life and consciousness. An interview with Karl Friston (by Martin Fortier & Daniel…

…的<ref name="Physiology1">{{cite book |author=Friedrich C |title=Physiology and genetics of sulfur-oxidizing bacteria |journal=Adv Microb Physiol |volume=3 …Berardinis RJ | title = Understanding the Intersections between Metabolism and Cancer Biology | journal = Cell | volume = 168 | issue = 4 | pages = 657–

…(2006). Unifying constructal theory for scale effects in running, swimming and flying. Journal of Experimental Biology, 209(2), 238-248.]

…chical Nb₃O₇(OH) superstructures with semiconductive and photoactive properties| journal= Journal of Materials Chemistry A| volume= …r=Feltz, Bernard |display-authors=etal |date=2006 |title=Self-organization and Emergence in Life Sciences |isbn=978-1-402-03916-4 |page=1}}</ref>

…cientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review |publisher=Dover Publications |location=New York |year= |isbn=0-486-

…ook|last=Morgan|first=Stephen|author2=Winship, Chris|title=Counterfactuals and Causal inference|publisher=Cambridge University Press|year=2007|isbn=978-0- …and effect, a time-order relationship with the cause preceding the effect, and the elimination of plausible alternative causes."<ref name=psy>{{cite book|

…thor-link1=Thomas M. Cover |last2=Thomas |first2=Joy A. |title=Elements of Information Theory |edition=2nd |location=New York |publisher=[[Wiley-Interscience]] |d

…ers》上的论文中提出的，<ref name=Bak1987>{{cite journal | author =Per Bak, Chao Tang and Kurt Wiesenfeld | year = 1987 | title = Self-organized criticality: an expl …er Bak, and Maya Paczuski | year = 1995 | title = Complexity, contingency, and criticality | journal =Proc Natl Acad Sci U S A | volume = 92 | pages = 66

…wiki.org/wiki/Expectation_of_Poisson_Distribution Proof wiki: expectation] and [http://www.proofwiki.org/wiki/Variance_of_Poisson_Distribution Proof wiki:

…ook|last=Morgan|first=Stephen|author2=Winship, Chris|title=Counterfactuals and Causal inference|publisher=Cambridge University Press|year=2007|isbn=}}</re

#[[The Ising model and the maximum entropy distribution]] #[[Mean-field approximation and the Curie-Weiss model]]

…u. Travel mode choice: a data fusion model using machine learning methods and evidence from travel diary survey data. Transportmetrica A. 2019, 10.1080/2 …Wen-Xu Wang*, Zi-You Gao*, Ying-Cheng Lai*. Universal model of individual and population mobility on diverse spatial scales. Nature Communications. 2017,

…first1=T.|last2=et.|first2=al.|title=Adaptation to the edge of chaos with random-wavelet feedback|journal=J. Phys. Chem. A|date=2009|doi=10.1021/jp804420g

…|year=1985 |last1=Černý |first1=V. |journal=Journal of Optimization Theory and Applications |volume=45 |pages=41–51}}</ref> 这种方法是对[[Metropol …|last3=Rasson |first3=J.-P. |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |volume=16 |issue=6 |pages=652–656}}</ref> 然而，

…同划分会导致A和B的状态空间就不一样，所以应该做一个归一化处理，即除以A和B最大熵值中较小的那一个。于是，我们可以有一个最小信息划分（minimum information bipartition，MIB）。整合程度<math>\Phi</math>定义如下：

…theorem'''（或无噪声编码定理）建立了可能的'''数据压缩 data compression '''的极限，以及'''香农熵 Shannon entropy'''的操作意义。 …Cover">Cover, Thomas M. (2006). "Chapter 5: Data Compression". Elements of Information Theory. John Wiley & Sons. ISBN 0-471-24195-4.</ref>):

RandomNum(Integer N){ R= Random(0,1);