Mathematical Theory of Nonequilibrium Steady States

Preface. - Introduction. - Circulation Distribution, Entropy Production and Irreversibility of Denumerable Markov Chains. - Circulation Distribution, Entropy Production and Irreversibility of Finite Markov Chains with Continuous Parameter. - General Minimal Diffusion Process: its Construction, Invariant Measure, Entropy Production and Irreversibility. - Measure-theoretic Discussion on Entropy Production of Diffusion Processes and Fluctuation-dissipation Theorem. - Entropy Production, Rotation Numbers and Irreversibility of Diffusion Processes on Manifolds. - On a System of Hyperstable Frequency Locking Persistence under White Noise. - Entropy Production and Information Gain in Axiom A Systems. - Lyapunov Exponents of Hyperbolic Attractors. - Entropy Production, Information Gain and Lyapunov Exponents of Random Hyperbolic Dynamical Systems. - References. - Index.