Boltzmann factor via state energy and temperature¶

The Boltzmann factor weights how likely a system is to occupy a micro-state of a given energy at thermal equilibrium.

Notation:

\(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

Equilibrium temperature is positive.

Links:

Wikipedia – Boltzmann distribution

boltzmann_factor¶: boltzmann_factor.

Symbol:: f
Latex:: \(f\)
Dimension:: dimensionless

energy_of_state¶: energy of state \(i\).

Symbol:: E[i]
Latex:: \(E_{i}\)
Dimension:: energy

equilibrium_temperature¶: temperature of the system at equilibrium.

Symbol:: T
Latex:: \(T\)
Dimension:: temperature

definition¶

f = exp(-E[i] / (k_B * T))

Latex:: \[f = \exp{\left(- \frac{E_{i}}{k_\text{B} T} \right)}\]