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Jozsef Beck
Equidistribution Of Dynamical Systems: Time-quantitative Second Law
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3040367Equidistribution Of Dynamical Systems: Time-quantitative Second Lawhttps://www.gandhi.com.mx/equidistribution-of-dynamical-systems-time-quantitative-second-law-9789811225574/phttps://gandhi.vtexassets.com/arquivos/ids/3584654/d791a9e7-556d-44a0-88a9-604f3d2c400a.jpg?v=63838558658373000020562284MXNWorld Scientific Publishing CompanyInStock/Ebooks/<p>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 readers 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.</p>...2976471Equidistribution Of Dynamical Systems: Time-quantitative Second Law20562284https://www.gandhi.com.mx/equidistribution-of-dynamical-systems-time-quantitative-second-law-9789811225574/phttps://gandhi.vtexassets.com/arquivos/ids/3584654/d791a9e7-556d-44a0-88a9-604f3d2c400a.jpg?v=638385586583730000InStockMXN99999DIEbook20209789811225574_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_<p>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 readers 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.</p>(*_*)9789811225574_<p>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 readers 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.</p>...9789811225574_World Scientific Publishing Companylibro_electonico_a58311c2-06bc-322a-9a80-3db222285d7c_9789811225574;9789811225574_9789811225574Jozsef BeckInglésMéxicohttps://getbook.kobo.com/koboid-prod-public/worldscientific-epub-49fe28ba-ed2e-4f8a-aa4f-e946887d6ab5.epub2020-10-05T00:00:00+00:00World Scientific Publishing Company