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Equidistribution of Dynamical Systems
Hardcover
Series: Fractals and Dynamics in Mathematics, Science, and the Arts:, Book 7
ISBN13: 9789811225550
Publisher: World Scientific Publishing Company
Published: Oct 16 2020
Pages: 448
Weight: 1.69
Height: 1.00 Width: 6.00 Depth: 9.00
Language: English
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.
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