Applied Mathematics

Learn Statistical Mechanics

How the behaviour of $10^{23}$ particles follows from counting: microstates and Boltzmann's entropy, the microcanonical ensemble and what temperature is, the Boltzmann distribution derived from a heat bath, free energy as the competition between energy and entropy, equipartition, the ideal gas and the Gibbs paradox, Maxwell-Boltzmann speeds, fluctuations and the thermodynamic limit, the grand canonical ensemble, Fermi-Dirac and Bose-Einstein statistics, the degenerate Fermi gas, Bose-Einstein condensation, the Ising model and the transfer matrix, mean-field theory and its failures, critical exponents and universality, Landau theory, the renormalisation group, and the H-theorem.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Statistical Mechanics

Microstates, macrostates and multiplicityThe microcanonical ensemble and temperatureDeriving the Boltzmann distributionFree energyEquipartition and heat capacityThe ideal gas and the Gibbs paradoxThe Maxwell-Boltzmann speed distributionFluctuations and the thermodynamic limitThe grand canonical ensembleFermi-Dirac and Bose-Einstein statisticsThe degenerate Fermi gasBose-Einstein condensationThe Ising model and the transfer matrixMean-field theoryCritical exponents and universalityLandau theoryThe renormalisation groupThe H-theorem and the arrow of time
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Statistical Mechanics exactly where it's useful.

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