.. index:: Statistical Mechanics

Week 1
==============

.. index::
   Statistical Mechanics, Mechanics, Probability, Boltzmann Factor

Section Title
--------------------


Why is statistics important? Remember we are dealing with Avogadro's number of DoFs. If we are going to calculate the dynamics of this system by calculating the dynamics of each particles. To store one screenshot of the system with each DoF take only 8 bits, we need :math:`10^23` bytes that is :math:`10^17` GB. It is not even possible to store only one screenshot of the system. So time to change our view of these kind of systems.

.. figure:: ../_static/newtonsDream.jpg
   :alt: Newton's Dream

   Newton's plan of mechanics. Mechanics was in the center of all physics.

What is mechanics? It deals with dynmaics in the following way:

* Description of initial state
* Time evolution of the system
* Extraction of observables



Test Math

.. math::

    {\d p^\alpha\over\d V} = -T^\alpha{}_\beta u^\beta

and the energy density that he measures is:

.. math::

    \rho = {E\over V} = -{u^\alpha p_\alpha \over V}
    = - u^\alpha {\d p_\alpha\over\d V}
    = u^\alpha T_{\alpha\beta} u^\beta