Boltzmann factor via state energy and temperature

The Boltzmann factor is an exponential factor that appears in many formulas of statistical physics and thermodynamics, e.g. the canonical partition function of a classical discrete system.

Notation:

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

Links:

  1. Wikipedia.

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

Equilibrium temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

definition

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

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