Tuckerman M. Statistical Mechanics. Theory and Molecular Simulation 2023

Textbook in PDF format

Scientists are increasingly finding themselves engaged in research problems that cross the traditional disciplinary lines of physics, chemistry, biology, materials science, and engineering. Because of its broad scope, statistical mechanics is an essential tool for students and more experienced researchers planning to become active in such an interdisciplinary research environment. Powerful computational methods that are based in statistical mechanics allow complex systems to be studied at an unprecedented level of detail. This book synthesizes the underlying theory of statistical mechanics with the computational techniques and algorithms used to solve real-world problems and provides readers with a solid foundation in topics that reflect the modern landscape of statistical mechanics. Topics covered include detailed reviews of classical and quantum mechanics, in-depth discussions of the equilibrium ensembles and the use of molecular dynamics and Monte Carlo to sample classical and quantum ensemble distributions, Feynman path integrals, classical and quantum linear-response theory, nonequilibrium molecular dynamics, the Langevin and generalized Langevin equations, critical phenomena, techniques for free energy calculations, machine learning models, and the use of these models in statistical mechanics applications. The book is structured such that the theoretical underpinnings of each topic are covered side by side with computational methods used for practical implementation of the theoretical concepts.
Classical mechanics
Theoretical foundations of classical statistical mechanics
The microcanonical ensemble and introduction to molecular dynamics
The canonical ensemble
The isobaric ensembles
The grand canonical ensemble
Monte Carlo
Free-energy calculations
Quantum mechanics
Quantum ensembles and the density matrix
Quantum ideal gases: Fermi-Dirac and Bose-Einstein statistics
The Feynman path integral
Classical time-dependent statistical mechanics
Quantum time-dependent statistical mechanics
The Langevin and generalized Langevin equations
Discrete models and critical phenomena
Introduction to machine learning in statistical mechanics