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:**

#. :math:`k_\text{B}` (:code:`k_B`) is :attr:`~symplyphysics.quantities.boltzmann_constant`.

**Conditions:**

#. Equilibrium temperature is positive.

**Links:**

#. `Wikipedia – Boltzmann distribution <https://en.wikipedia.org/wiki/Boltzmann_distribution>`__

.. py:currentmodule:: symplyphysics.statistical_physics.ensembles.canonical.boltzmann_factor_via_state_energy_and_temperature

.. py:data:: boltzmann_factor

    :attr:`~symplyphysics.symbols.thermodynamics.boltzmann_factor`.

Symbol:
    :code:`f`

Latex:
    :math:`f`

Dimension:
    :code:`dimensionless`


.. py:data:: energy_of_state

    :attr:`~symplyphysics.symbols.basic.energy` of state :math:`i`.

Symbol:
    :code:`E[i]`

Latex:
    :math:`E_{i}`

Dimension:
    :code:`energy`


.. py:data:: equilibrium_temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the system at equilibrium.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: law

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


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