## Lecture notes from Dr. Roundy's 2014 course website:

Most thermodynamic quantities can be expressed as weighted averages over all possible eigenstates (or microstates). For instance, the internal energy is given by: by: $$U = \sum_i P_i E_i$$ Note that this will probably not be an eigenvalue of the energy, but that's okay. The energy eigenvalues are so close for the total energy of a macroscopic object that we couldn't distinguish them anyhow. Any thermodynamic quantity that is defined for a microstate will be computed using precisely this sort of average: this will also cover magnetization and pressure, for instance, or the intensity of electromagnetic radiation at a given frequency.

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