Research proof index

The mean energy is the negative derivative of the logarithm of the (mathematical) partition function with respect to β = 1/(kB T). see: Tong (§1.3.2, §1.3.3), L&L (§31, implicitly, and §36) Here the derivative is a derivWithin over Set.Ioi 0 since β > 0.

The mean energy can be expressed as a ratio of integrals.

Fundamental relation between thermodynamic and differential entropy: S_thermo = S_diff - kB * dof * log h.

In the finite, nonempty case the thermodynamic and Shannon entropies coincide. All semi-classical correction factors vanish (dof = 0, phaseSpaceUnit = 1), so the absolute thermodynamic entropy reduces to the discrete Shannon form.

Probability of the first state (energy E₀) in closed form.

Probability of the second state (energy E₁) in closed form.