Skip to main content
  • Book
  • © 2004

Mathematical Theory of Nonequilibrium Steady States

On the Frontier of Probability and Dynamical Systems

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1833)

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (11 chapters)

  1. Front Matter

    Pages I-IX
  2. Introduction

    • Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 1-10
  3. 6 On a System of Hyperstable Frequency Locking Persistence under White Noise

    • Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 149-158
  4. 7 Entropy Production and Information Gain in Axiom A Systems

    • Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 159-188
  5. 8 Lyapunov Exponents of Hyperbolic Attractors

    • Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 189-214
  6. References

    • Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 253-276
  7. Back Matter

    Pages 277-280

About this book

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.

Keywords

  • Markov chain
  • Markov processes
  • diffusion process
  • entropy production rate
  • hyperbolic dynamical systems
  • irreversibility
  • nonequilibrium statistical physics
  • statistical physics

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions