A Road To Randomness In Physical Systems
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A Road To Randomness In Physical Systems
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Author : Eduardo M.R.A. Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Road To Randomness In Physical Systems written by Eduardo M.R.A. Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
There are many ways of introducing the concept of probability in classical, i. e, deter ministic, physics. This work is concerned with one approach, known as "the method of arbitrary funetionJ. " It was put forward by Poincare in 1896 and developed by Hopf in the 1930's. The idea is the following. There is always some uncertainty in our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. A probability density may be used to describe this uncertainty. For many physical systems, dependence on the initial density washes away with time. Inthese cases, the system's position eventually converges to the same random variable, no matter what density is used to describe initial uncertainty. Hopf's results for the method of arbitrary functions are derived and extended in a unified fashion in these lecture notes. They include his work on dissipative systems subject to weak frictional forces. Most prominent among the problems he considers is his carnival wheel example, which is the first case where a probability distribution cannot be guessed from symmetry or other plausibility considerations, but has to be derived combining the actual physics with the method of arbitrary functions. Examples due to other authors, such as Poincare's law of small planets, Borel's billiards problem and Keller's coin tossing analysis are also studied using this framework. Finally, many new applications are presented.
A Road To Randomness In Physical Systems
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Author : Eduardo M R a Engel
language : en
Publisher:
Release Date : 1992-02-01
A Road To Randomness In Physical Systems written by Eduardo M R a Engel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-01 with categories.
Randomness And Undecidability In Physics
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Author : Karl Svozil
language : en
Publisher: World Scientific
Release Date : 1993-10-05
Randomness And Undecidability In Physics written by Karl Svozil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-05 with Science categories.
Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an “inner description”, a “virtual physics” of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as “randomness” in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the “distant future”. In other words: no “speedup” or “computational shortcut” is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.
Randomnicity
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Author : Anastasios A Tsonis
language : en
Publisher: World Scientific
Release Date : 2008-09-18
Randomnicity written by Anastasios A Tsonis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-18 with Science categories.
This unique book explores the definition, sources and role of randomness. A joyful discussion with many non-mathematical and mathematical examples leads to the identification of three sources of randomness: randomness due to irreversibility which inhibits us from extracting whatever rules may underlie a process, randomness due to our inability to have infinite power (chaos), and randomness due to many interacting systems. Here, all sources are found to have something in common: infinity. The discussion then moves to the physical system (our universe). Through the quantum mechanical character of small scales, the second law of thermodynamics and chaos, randomness is shown to be an intrinsic property of nature — this is consistent with the three sources of randomness identified above. Finally, an explanation is given as to why rules and randomness cannot exist by themselves, but instead have to coexist. Many examples are presented, ranging from pure mathematical to natural and social processes, that clearly demonstrate how the combination of rules and randomness produces the world we live in. Contents: The Three Parts of EverythingSources of RandomnessRandomness in the UniverseThe Emergence of Real WorldThe Role of Randomness Readership: Academic and general public. Keywords:Randomness;Chaos;Fractals;Determinism;Natural ProcessesKey Features:Differs from other books on this subject in that it treats randomness from a complex systems point of view rather than from a solely probabilistic oneSuitable for the general public with an interest in scienceUseful for scientists in all areasReviews:“Reading the book is like visiting a museum, and as the reader goes successively through the chapters he (or she) encounters beautiful ideas and interesting comments. Although the book is not a book on the history of mathematics, it contains interesting historical facts.”Zentralblatt MATH “I recommend reading it to those who want a quick introduction to ideas about randomness and those whose exposure to these ideas has been piecemeal, as mine was. The book may spark the imaginations of readers and advance our science through innovative application of the concepts. Someone might just find life-changing inspiration.”Vadose Zone Journal “As a contribution to popular science this book is welcome. Tsonis explains randomness as it enters into mathematics, science and everyday life.”Mathematical Reviews
Dynamics Of Gambling Origins Of Randomness In Mechanical Systems
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Author : Jaroslaw Strzalko
language : en
Publisher: Springer
Release Date : 2010-01-14
Dynamics Of Gambling Origins Of Randomness In Mechanical Systems written by Jaroslaw Strzalko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Science categories.
Our everyday life is in?uenced by many unexpected (dif?cult to predict) events usually referred as a chance. Probably, we all are as we are due to the accumulation point of a multitude of chance events. Gambling games that have been known to human beings nearly from the beginning of our civilization are based on chance events. These chance events have created the dream that everybody can easily become rich. This pursuit made gambling so popular. This book is devoted to the dynamics of the mechanical randomizers and we try to solve the problem why mechanical device (roulette) or a rigid body (a coin or a die) operating in the way described by the laws of classical mechanics can behave in such a way and produce a pseudorandom outcome. During mathematical lessons in primary school we are taught that the outcome of the coin tossing experiment is random and that the probability that the tossed coin lands heads (tails) up is equal to 1/2. Approximately, at the same time during physics lessons we are told that the motion of the rigid body (coin is an example of suchabody)isfullydeterministic. Typically,studentsarenotgiventheanswertothe question Why this duality in the interpretation of the simple mechanical experiment is possible? Trying to answer this question we describe the dynamics of the gambling games based on the coin toss, the throw of the die, and the roulette run.
Introduction To Random Time And Quantum Randomness
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Author : Kai Lai Chung
language : en
Publisher: World Scientific
Release Date : 2003
Introduction To Random Time And Quantum Randomness written by Kai Lai Chung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown. In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.
Introduction To Random Time And Quantum Randomness
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language : en
Publisher:
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Introduction To Random Time And Quantum Randomness written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Theory And Simulation Of Random Phenomena
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Author : Ettore Vitali
language : en
Publisher: Springer
Release Date : 2018-06-13
Theory And Simulation Of Random Phenomena written by Ettore Vitali and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-13 with Science categories.
The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.
Random And Quasi Random Point Sets
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Author : Peter Hellekalek
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-10-09
Random And Quasi Random Point Sets written by Peter Hellekalek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-09 with Mathematics categories.
This book sumarizes recent theoretical and practical developments. The generation and the assessment of pseudo- and quasi-random point sets is one of the basic tasks of applied mathematics and statistics, with implications for Monte Carlo methods, stochastic simulation, and applied statistics. They are also of strong theoretical interest, with applications to algebraic geometry, metric number theory, probability theory, and cryptology.
Lectures On Random Voronoi Tessellations
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Author : Jesper Moller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Random Voronoi Tessellations written by Jesper Moller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.