Molecular Simulation

Computing the properties of molecular systems.

Part I · Equilibrium

The Boltzmann Distribution Microstates, partition functions, free energy, and why sampling is the central problem of statistical mechanics

The Monte Carlo Method Metropolis–Hastings, detailed balance, Markov chains, and the canonical ensemble

Molecular Dynamics Hamilton's equations, symplectic integrators, thermostats, and the ergodic hypothesis

Part II · The Sampling Problem

The Energy Landscape Rugged surfaces, local minima, barriers, and why naive simulation gets trapped

Enhanced Sampling Umbrella sampling, replica exchange, metadynamics, and the art of choosing collective variables

Free Energy Methods Perturbation theory, thermodynamic integration, and alchemical transformations

Rare Events Transition path theory, forward flux sampling, and the statistics of infrequent transitions

Part III · Beyond Classical Simulation

Non-Equilibrium Statistical Mechanics The Jarzynski equality, Crooks fluctuation theorem, and extracting equilibrium from irreversible work

Coarse-Graining Effective degrees of freedom, systematic reduction, and the multiscale hierarchy

Machine Learning and Simulation Neural network potentials, learned collective variables, Boltzmann generators, and the convergence with generative flows