Statistical weight of macrostate

If a physical system can be described as having several states which can be occupied by different numbers of particles but with the total number of particles being conserved and a condition that all allowed microstates of the closed system are equiprobable, the formula for the statistical weight of the system can be found in combinatorics.

Notes:

1. Law can also be represented in form \(\\Omega = \frac{N!}{\prod_i (N_i!)}\) (Omega = factorial(N) / Product(factorial(N_i), i))

Links:

1. Chemistry LibreTexts, formula 1.5.1.

statistical_weight

statistical_weight of the system’s macrostate.

Symbol:

Omega

Latex:

\(\Omega\)

Dimension:

dimensionless

particle_count_in_state

particle_count in state \(i\).

Symbol:

N[i]

Latex:

\({N}_{i}\)

Dimension:

dimensionless

law

Omega = factorial(Sum(N[i], i)) * Product(factorial(N[i]), i)^(-1)

Latex:

\[\Omega = \sum_i {N}_{i}! \prod_i {N}_{i}!^{-1}\]