Nonequilibrium Statistical Mechanics
Description
This book covers basic and advanced concepts of nonequilibrium statistical physics.
The first part is addressed to undergraduate students: it begins introducing - historically and technically - Langevin equations and general stochastic processes with emphasis on their significance in physics, then it explains kinetic theory and how irreversibility emerges for systems with many interacting particles; it continues with the theory of fluctuations from Einstein to Onsager, with linear response theory including the most recent generalisations to nonequilibrium systems, and finally the fundamental topics in stochastic thermodynamics, from entropy production to fluctuation relations, are presented.
The second part involves advanced topics, necessary to deal with the state-of-the-art approaches in nonequilibrium statistical physics. A detailed discussion is devoted to the problem of building nonequilibrium stochastic models through coarse-graining methods from microscopic descriptions as well as from experimental or numerical data. The last three chapters are dedicated to applications: one describes climate and systems with multiple time scales, with excursus into information theory and causation; another chapter deals with granular and active matter, with several examples where the general concepts (illustrated in the first part) come to life in simulations and experiments; and finally the last chapter discusses non-intuitive phenomena that can appear out of equilibrium, including negative differential and absolute mobility.
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Persons
Dr Andrea Puglisi, a Marie Curie fellow at Orsay, Paris (2003-2004) and a postdoc at Sapienza University (2005-2008), has served as director of research at the Institute of Complex Systems of the National Research Council in Rome (CNR-ISC) sine 2021. His expertise are granular materials (theory and experiments), nonequilibrium statistical mechanics, and computational cognitive science and has co-authored over 150 scientific papers and two books.
Prof. Alessandro Sarracino, postdoc in Rome at ISC - CNR (2010-2013) and in Paris at LPTMC Sorbonne Université (2014-2015), has been researcher at ISC - CNR (2016-2018) and at University of Campania "L. Vanvitelli" (2018-2022). Since 2022, he has been an Associate Professor at the University of Campania. Having co-authored over 70 scientific papers, his expertise includes nonequilibrium statistical mechanics, with a focus on granular and disordered systems, active matter, anomalous transport, and neural networks.
Prof. Angelo Vulpiani graduated from Rome University in 1977, and has been a CNR fellow, Assistant Professor, and Associate Professor at various universities. He is currently a Professor of Theoretical Physics at Sapienza University of Rome. His research interests include chaos and complexity in dynamical systems, nonequilibrium statistical mechanics, turbulence, transport, and diffusion. He has authored approximately 300 scientific papers and eleven books. In 2021, he received the EPS Statistical and Nonlinear Physics Prize, the 2023 Lewis Fry Richardson Medal, and has been a Fellow of the Institute of Physics since 2004.
Content
Part One
1) Brownian Motion: introduction to the phenomenon, the Einstein relation, the Langevin approach, the historical relevance of the problem and its role in stochastic processes. 2) Boltzmann Equation: a sketch of the derivation from microscopic level, H-theorem and related paradoxes, Ehrenfest model and modern developments (Lanford theorem), the many faces of entropy. 3) Onsager Relations : Einstein fluctuation theory and the role of time-reversal symmetry in the building of stochastic equations, the connection with detailed balance condition. 4) Fluctuation-Dissipation Relations : a sketch of the general formulation and how Fluctuation-Dissipation Relations in classical Hamiltonian and Markovian stochastic processes are obtained. 5) Fluctuation Theorems: an introduction to Fluctuation Theorems and entropy production
Part Two
6) Model Building : Langevin equations from microscopic description, the Smoluchovski, van Kampen and Zwanzig approaches; 7) Causality and inference: applications of Fluctuation-Dissipation relations to the problem of causality and inference in data analysis; 8) Systems with multiple scales: transport and diffusion problems and applications to climate; 9) Non-Hamiltonian systems: granular materials and active matter that includes systems of self-propelled particles at all scales (micro-swimmers, fishes, insects, birds, sperms). 10) Stranger Things : a miscellanea of non-intuitive phenomena, such as friction-driven motors and negative response.
