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:**

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

**Links:**

#. `Chemistry LibreTexts, formula 1.5.1 <https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_(Smirnov_and_McCarty)/01%3A_Biochemical_Thermodynamics/1.05%3A_The_Boltzmann_Distribution_and_the_Statistical_Definition_of_Entropy>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.maxwell_boltzmann_statistics.statistical_weight_of_macrostate

.. py:data:: statistical_weight

    :attr:`~symplyphysics.symbols.thermodynamics.statistical_weight` of the system's macrostate.

Symbol:
    :code:`Omega`

Latex:
    :math:`\Omega`

Dimension:
    :code:`dimensionless`


.. py:data:: particle_count_in_state

    :attr:`~symplyphysics.symbols.basic.particle_count` in state :math:`i`.

Symbol:
    :code:`N[i]`

Latex:
    :math:`{N}_{i}`

Dimension:
    :code:`dimensionless`


.. py:data:: law

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


    Latex:
        .. math::
            \Omega = \sum_i {N}_{i}! \prod_i {N}_{i}!^{-1}