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Books > Science & Mathematics > Physics > Thermodynamics & statistical physics > Thermodynamics
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Equidistribution Of Dynamical Systems: Time-quantitative Second Law (Hardcover)
Loot Price: R4,038
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Equidistribution Of Dynamical Systems: Time-quantitative Second Law (Hardcover)
Series: Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications, 7
Expected to ship within 10 - 15 working days
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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.
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