Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems

Min Qian, Da-Quan Jiang, “Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems”
2004 | ISBN-10: 3540206116 | 296 pages | PDF | 1 MB

This volume provides a systematic mathematical exposition of the conceptual problems of nonequilibrium statistical physics, such as entropy production, irreversibility, and ordered phenomena. Markov chains, diffusion processes, and hyperbolic dynamical systems are used as mathematical models of physical systems. A measure-theoretic definition of entropy production rate and its formulae in various cases are given. It vanishes if and only if the stationary system is reversible and in equilibrium. Moreover, in the cases of Markov chains and diffusion processes on manifolds, it can be expressed in terms of circulations on directed cycles. Regarding entropy production fluctuations, the Gallavotti-Cohen fluctuation theorem is rigorously proved.

Chance: The science and secrets of luck, randomness and probability

New Scientist, “Chance: The science and secrets of luck, randomness and probability”
2015 | ISBN: 1781255431 | 272 pages | EPUB, MOBI | 1 MB

For you to be here today reading this requires a mind-boggling series of lucky breaks, starting with the Big Bang and ending in your own conception. So it’s not surprising that we persist in thinking that we’re in with a chance, whether we’re playing the lottery or working out the likelihood of extra-terrestrial life.

In Chance, a (not entirely) random selection of the New Scientist’s sharpest minds provide fascinating insights into luck, randomness, risk and probability. From the secrets of coincidence to placing the perfect bet, the science of random number generation to the surprisingly haphazard decisions of criminal juries, it will explore these, and many other, tantalising questions.

Following on from the bestselling Nothing and Question Everything, this book will open your eyes to the weird and wonderful world of chance – and help you see when some things, in fact, aren’t random at all.