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In order to apply atomic mechanism to the system subjected to the
process in thermodynamics and statistical thermodynamics, it is necessary
that the atomic mechanisms of the process fall into one of following two
classes:

those so rapid that, in the time frame of the process of interest, the atomic
states effectively visit all of their accessible range, bringing the system to
its state of internal thermodynamic equilibrium; and

those so slow that their progress can be neglected in the time frame of the
process of interest.
The rapid atomic mechanisms represent the internal energy of the
system. They mediate the macroscopic changes that are of interest for

thermodynamics and statistical thermodynamics because they quickly
bring the system close enough to thermodynamic equilibrium. "When
intermediate rates are present, thermodynamics and statistical mechanics

cannot be applied." Such intermediate rate atomic processes do not bring
the system near enough to thermodynamic equilibrium in the time frame of
the macroscopic process of interest. This separation of time scales of

atomic processes is a theme that recurs throughout the subject.
For example, classical thermodynamics is characterized by its study of
materials that have equations of state or characteristic equations. They

express equilibrium relations between macroscopic mechanical variables
and temperature and internal energy. They express the constitutive
peculiarities of the material of the system. A classical material can usually
be described by a function that makes pressure dependent on volume and

temperature, the resulting pressure being established much more rapidly
than any imposed change of volume or temperature.
The present article takes a gradual approach to the subject, starting with a

focus on cyclic processes and thermodynamic equilibrium, and then
gradually beginning to further consider non-equilibrium systems.

2.2 Internal Energy

In thermodynamics, the internal energy is the total energy

contained by a thermodynamic system. Internal energy has two such major
components as kinetic energy and potential energy. The kinetic energy is
caused by the motion of the system of particles and the potential energy is

associated with the static rest mass energy of the constituents of matter,
static electric energy of atoms within molecules or crystals, and the static

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