This textbook offers a clear, unified introduction to nonequilibrium statistical mechanics. It combines the classical foundations of equilibrium and nonequilibrium thermodynamics with the field's latest advances. Key topics include Brownian motion, fluctuations theory, the Boltzmann equation, and probability measures in phase space. A common mathematical framework links linear-response theory, transport processes, large-deviation principles, and stochastic dynamics.

A companion Volume II will extend the discussion to applications such as anomalous transport, living matter, molecular dynamics, and open quantum systems.

The book is written for researchers in applied mathematics, theoretical physics, biophysics, and theoretical chemistry who study nonequilibrium phenomena. It is equally suited to graduate students seeking an accessible path to advanced topics in thermodynamics, transport theory, fluctuation dynamics, and dissipation. It also serves as a reference for graduate courses on statistical mechanics, stochastic systems, and quantum thermodynamics.

Offers a modern, integrated approach to nonequilibrium phenomena Emphasizes the role of scales and their influence on the development of nonequilibrium theories Highlights the connections and distinctions between stochastic processes and dynamical systems

Autorentext

Carlos Mejía-Monasterio is a Professor of Physics and Mathematics at the Technical University of Madrid, Spain. His research lies at the intersection between statistical physics, dynamical systems and stochastic processes, with significant contributions to nonequilibrium statistical mechanics. His work explores how macroscopic phenomena emerge from microscopic dynamics, covering topics such as low-dimensional transport, nonequilibrium fluctuations, stochastic thermodynamics, active transport, and interacting particle systems.

Lamberto Rondoni is Professor of Mathematical Physics at Politecnico di Torino, Italy. He specializes in nonequilibrium statistical mechanics and its applications across science and technology. He has contributed to the development of the theory of fluctuations and the theory of response to perturbations for nonequilibrium systems, with applications ranging from nanotechnology to climate science. He has also worked on kinetic theory and transport phenomena. He is interested in the foundations of Physics, in the theory of equivalence of ensembles and in the relation between deterministic and stochastic models. He has published various popular essays.

Inhalt

1. Introduction.- 2. Hydrodynamics and nonequilibrium thermodynamics.- 3. The Brownian motion and its legacy.- 4. Energy equipartition, virial theorem and Boyle's law.- 5. Probabilities in phase space.- 6. Linear response theory.