.. index:: Gamma Space, mu Space, BBGKY

:math:`\Gamma` Space and :math:`\mu` Space
==============================================================================


Two Spaces
-----------------------------


Here we have a table comparing the two spaces: :math:`\Gamma` space and :math:`\mu` space. (More about :math:`\mu` space and :math:`\Gamma` space, :ref:`mu-space-and-gamma-space`.)

+-----------------------+-----------------------------------------------------------+-----------------------------------+
|      Two Spaces       | :math:`\Gamma` space                                      |  :math:`\mu` space                |
+=======================+===========================================================+===================================+
|  Dimensions           |  :math:`6 N`                                              |   :math:`6`                       |
+-----------------------+-----------------------------------------------------------+-----------------------------------+
|  State of system      |   A point                                                 |  :math:`N` points                 |
+-----------------------+-----------------------------------------------------------+-----------------------------------+
|  Probability density  | :math:`\rho(q^n_i, p^n_i; t)`                             |  :math:`f_n(q_i,p_i; t)`          |
+-----------------------+-----------------------------------------------------------+-----------------------------------+
|  Observables          |  Difference in the integration                                                                |
+-----------------------+-----------------------------------------------------------+-----------------------------------+
|  EoM                  | Liouville equation or Von Neumann equation                |   BBGKY Hierarchy                 |
+-----------------------+-----------------------------------------------------------+-----------------------------------+