Thermodynamics of Chaos and Order (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)

The discovery of chaotic motion in low-dimensional systems raised the question: What kind of thermodynamics describes a system if it is neither ergodic nor Hamiltonian or possesses a finite number of degrees of freedom? This Monographs is the first to discuss this question. Classical thermodynamics and statistical mechanics were developed for ergodic Hamiltonian systems with a very large number of degrees of freedom. The discovery of chaotic motion in low-dimensional systems raised the question: what kind of thermodynamics describes a system if it is neither ergodic nor Hamiltonian or possesses a finite number of degrees of freedom? The book is the first to discuss this question. The specific features of this book are a detailed consideration of the Einstein formula linking entropy and probability, a circumstantial discussion of the Fermi-Pasta-Ulam problem and an elaborated version of the statistical mechanics of ideal fluid. The early chapters of the book do not require any knowledge beyond the standard calculus course Thermodynamics employs two concepts nonexistent in classical mechanics: temperature and entropy.