Physics / advanced
Ensembles and the statistics of matter
Derive equilibrium predictions through counting, partition functions, ensemble transformations, and the distinct statistics of classical and quantum particles.
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Module 01 advanced
Ensembles and the statistics of matter
Derive equilibrium predictions through counting, partition functions, ensemble transformations, and the distinct statistics of classical and quantum particles.
- 01
Count physical states in phase space
Normalize classical counting with Planck cells and remove permutation overcounting without confusing dilution with distinguishability.
32 min - 02
Find temperature by sharing a fixed energy
Derive thermal equilibrium from state multiplicities and distinguish bounded-spectrum negative temperatures from ordinary cooling.
32 min - 03
Derive Boltzmann weights from a reservoir
Expand reservoir entropy to obtain canonical probabilities, finite-reservoir corrections, and energy-fluctuation identities.
32 min - 04
Turn a state sum into an energy integral
Derive density-of-states normalization and use a Laplace transform to distinguish available states from occupied states.
32 min - 05
Let particles exchange with a reservoir
Derive grand-canonical weights and occupation laws while distinguishing an imposed chemical potential from a fixed particle number.
32 min - 06
Specify what ensemble equivalence means
Connect concentration and entropy concavity to bulk equivalence while preserving finite-size correlations and constraint-dependent fluctuations.
32 min - 07
Locate the ideal Bose condensation threshold
Separate the ground state from the continuum and state the dimensional and thermodynamic assumptions behind a condensation temperature.
32 min - 08
Expand about a filled Fermi sea
Derive zero-temperature filling and controlled low-temperature corrections at fixed particle density.
32 min - 09
Count thermal photons with zero chemical potential
Derive Planck energy density from mode counting and connect cavity energy, isotropic pressure, and surface emission.
32 min - 10
Read interactions through virial coefficients
Derive the second virial correction from a pair potential and keep density truncation separate from uncontrolled dense-fluid extrapolation.
32 min