Canonical partition function of a classical discrete system
===========================================================

Let us assume a canonical ensemble, i.e. a thermodynamically large system that is in thermal contact
with the environment, with a temperature T and whose volume and number of constituent particles remain
constant. For a classical discrete system the partition function is the sum of the Boltzmann factors
of all the possible energy states:

**Links:**

#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)#Classical_discrete_system>`__.

..
    NOTE replace `boltzmann_factor` with actual exponent?

.. py:currentmodule:: symplyphysics.laws.thermodynamics.canonical_partition_function_of_classical_discrete_system

.. py:data:: partition_function

    :attr:`~symplyphysics.symbols.thermodynamics.partition_function` of the system.

Symbol:
    :code:`Z`

Latex:
    :math:`Z`

Dimension:
    :code:`dimensionless`


.. py:data:: boltzmann_factor

    :attr:`~symplyphysics.symbols.thermodynamics.boltzmann_factor` of energy state :math:`i`. See :doc:`Boltzmann factor
    <definitions.boltzmann_factor_via_state_energy_and_temperature>`.

Symbol:
    :code:`f[i]`

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

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`Z = Sum(f[i], i)`


    Latex:
        .. math::
            Z = \sum_i {f}_{i}