Physics / advanced
Statistical physics and collective behavior
Build thermodynamics from ensembles, fluctuations, quantum statistics, phase transitions, and controlled nonequilibrium models.
Your route through physics
Follow the path or begin with a question. Every lesson is open.
Your place, at your pace. Progress is optional and saved only in this browser when available.
Read / explore / reason
Inside this module
Module 01 advanced
Statistical physics and collective behavior
Build thermodynamics from ensembles, fluctuations, quantum statistics, phase transitions, and controlled nonequilibrium models.
- 01
Entropy and the microcanonical ensemble
Count accessible states, define entropy and temperature, and distinguish typical behavior from a deterministic law for every small system.
29 min - 02
The canonical ensemble and partition function
Derive Boltzmann weights from a reservoir and extract energy, free energy, heat capacity, and fluctuations from one finite sum.
29 min - 03
The grand canonical ensemble
Treat particle exchange with a reservoir, interpret chemical potential, and connect number fluctuations to susceptibility.
30 min - 04
Classical gases and equipartition
Derive ideal-gas thermodynamics from phase space and identify the assumptions behind the energy-per-quadratic-mode rule.
30 min - 05
Bose and Fermi statistics
Derive ideal quantum occupation laws and connect exclusion, enhancement, and the dilute classical limit to mode counting.
30 min - 06
Fluctuations and equilibrium response
Relate measurable equilibrium variances to heat capacity and magnetic susceptibility, while separating static identities from dynamical response.
31 min - 07
The Ising model and mean-field theory
Derive self-consistent magnetization, test stability, and understand why replacing neighbors by an average misses important fluctuations.
32 min - 08
Critical scaling and universality
Read critical power laws, identify relevant scales, and understand how finite size and universality constrain real measurements.
32 min - 09
Kinetic theory and the Boltzmann equation
Follow a dilute gas through one-particle phase space, derive collision conservation rules, and distinguish kinetic relaxation from a fluid approximation.
33 min - 10
Nonequilibrium work and fluctuation relations
Derive the logic of exponential work averages, test Jarzynski's equality in an exact quench, and expose rare-event sampling limits.
33 min