Statistical Mechanics

Statistical mechanics from the ground up, starting from the fact that having many particles is enough to fix the outcome, and running through entropy, the partition function and quantum statistics. Read each piece as an article, or send it through one slide at a time.

Probability and large numbers

Many particles are enough to fix the outcome Counting the states gives you the odds

The microcanonical ensemble

In an isolated system every state weighs the same One line joining counting to thermodynamics Temperature is how fast the state count grows Mixing a gas with itself changes nothing With a ceiling above, the temperature turns negative Can sorting alone break the second law?

The canonical ensemble

Touch a heat bath and the odds turn exponential The partition function knows everything Energy fluctuations are the heat capacity Entropy rewritten in terms of probability At a settled temperature it is F that becomes smallest Settle nothing you do not know, and the distribution is settled

Applications

The ideal gas and the Maxwell distribution Half of kT for every degree of freedom A system with only two levels Oscillator heat capacity and where equipartition fails Lattice waves and the heat capacity of a solid

Phase transitions

Neighbours wanting to agree is all it takes The shape of a transition, without solving a model Two corrections to the ideal gas, and a liquid appears Laid in a line, no transition happens

Quantum statistics

Trading particles as well The Fermi and Bose distributions Electrons stay packed even when cold Black-body radiation and Planck's formula Bose-Einstein condensation A reaction stops when the chemical potentials come level Entropy has an absolute zero

Time and fluctuations

Gather up a great many random steps A grain shaken by molecules nobody can see Getting numbers out of a model nobody can solve What cannot be undone depends on how finely you look