| name | thermodynamics-statistical-mechanics |
| description | Solve and verify equilibrium thermodynamics and statistical mechanics problems using explicit systems, sign conventions, equations of state, thermodynamic potentials, ensembles, partition functions, fluctuations, and phase-equilibrium conditions. |
| license | MIT |
Thermodynamics and Statistical Mechanics
Define the system
- State boundary, open/closed/isolated status, phases, components, constraints, reservoirs,
state variables, equation of state, process path, and equilibrium assumptions.
- Declare heat/work sign conventions and distinguish state functions from path functions.
- Use absolute temperature and coherent units. Use
$cx-dimensional-analysis-units when scales vary.
- Decide whether a macroscopic thermodynamic or microscopic ensemble description is appropriate.
Thermodynamic route
- Apply the first law to the declared system, including matter flow and non-
pV work when present.
- Apply the second law through entropy balance; separate reversible equality from irreversible inequality.
- Select the natural potential for controlled variables: internal energy, enthalpy, Helmholtz,
or Gibbs free energy.
- Use exact differentials and Maxwell relations only for well-defined equilibrium state functions.
- For phase or reaction equilibrium, enforce temperature, pressure, and chemical-potential conditions.
Statistical route
- Define microstates, energy spectrum, degeneracy, conserved quantities, and selected ensemble.
- Construct and normalize the partition function or probability distribution.
- Derive observables and fluctuations from the same convention; state classical/quantum and
distinguishable/indistinguishable assumptions.
- Check thermodynamic-limit and low/high-temperature approximations before using them.
Verify
- Check extensivity/intensivity and Euler homogeneity where applicable.
- Check units, positivity of temperature/heat capacity assumptions, entropy production, and stability.
- Recover ideal-gas, dilute, noninteracting, zero-coupling, and large-system limits.
- Confirm probability normalization and fluctuation-response relations.
- Test that cycles satisfy energy conservation and the Clausius inequality.
- Distinguish equilibrium predictions from kinetics and finite-time transport.
Deliver
Report system definition, conventions, ensemble or potential, derivation, equilibrium/stability result,
checks, and applicability range. Do not infer microscopic mechanism from a successful equation-of-state fit.
Source basis
The workflow is an original synthesis informed by the thermodynamics and probability treatment in
Crowell's CC BY-SA Modern Physics; provenance is in ../../docs/TEXTBOOK_SOURCES.md.
