Equidistribution Of Dynamical Systems: Time-quantitative Second Law

Jozsef Beck (Autor)

Buch | Hardcover

448 Seiten

2020
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-12-2555-0 (ISBN)

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We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For example, what can we say about the typical time evolution of a large system starting from a stage far from equilibrium? What happens in a realistic time scale? The reader's first reaction is probably: What about the famous Second Law (of thermodynamics)?Unfortunately, there are plenty of notorious mathematical problems surrounding the Second Law. (1) How to rigorously define entropy? How to convert the well known intuitions (like 'disorder' and 'energy spreading') into precise mathematical definitions? (2) How to express the Second Law in forms of a rigorous mathematical theorem? (3) The Second Law is a 'soft' qualitative statement about entropy increase, but does not say anything about the necessary time to reach equilibrium.The object of this book is to answer questions (1)-(2)-(3). We rigorously prove a Time-Quantitative Second Law that works on a realistic time scale. As a by product, we clarify the Loschmidt-paradox and the related reversibility/irreversibility paradox.

Erscheinungsdatum	06.11.2020
Reihe/Serie	Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications ; 7
Verlagsort	Singapore
Sprache	englisch
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
ISBN-10	981-12-2555-9 / 9811225559
ISBN-13	978-981-12-2555-0 / 9789811225550
Zustand	Neuware