Entropy of independent subsystems is sum of their entropies
===========================================================

If a thermodynamic system can be decomposed into several subsystems which are all statistically
independent, the total entropy of the system can be calculated as the sum of the entropies of all
the subsystems. Mathematically speaking, this is a representation of such a property of entropy
known as `subadditivity <https://en.wikipedia.org/wiki/Subadditivity>`_.

**Conditions:**

#. The subsystems must be (approximately) independent in the statistical sense.

**Links:**

#. `ScienceDirect <https://www.sciencedirect.com/science/article/abs/pii/S0378437103002620>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.entropy_of_independent_subsystems_is_sum_of_their_entropies

.. py:data:: total_entropy

    Total :attr:`~symplyphysics.symbols.thermodynamics.entropy` of the system as a whole.

Symbol:
    :code:`S`

Latex:
    :math:`S`

Dimension:
    :code:`energy/temperature`


.. py:data:: subsystem_entropy

    :attr:`~symplyphysics.symbols.thermodynamics.entropy` of the :math:`i`-th subsystem.

Symbol:
    :code:`S[i]`

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

Dimension:
    :code:`energy/temperature`


.. py:data:: law

    :code:`S = Sum(S[i], i)`


    Latex:
        .. math::
            S = \sum_i {S}_{i}