Statistical Mechanics - Physics at Oregon State University

Chapter 1
Foundation of statistical
mechanics.
1.1 Introduction.
What is the difference?
In our study of thermodynamics we have derived relations between state
variables, response functions, and free energies. We have shown how a change
of variables affects the choice of free energy. We derived limitations on response
functions. Finally, we used equations of state to describe experiments. These
equations of state were either derived from experimental results (i.e. a good
guess of the functions) or from models of the free energy. At the heart of all
our derivations was the thermodynamic limit. Our systems have to be large
enough for fluctuations to be unimportant. In addition, we assume that we can
introduce the idea of reservoirs, which are external systems much larger than
the system we are investigating. In a manner of speaking, thermodynamics is
the theory of experimental measurements. It defines what we can measure, and
how results should be related.
In statistical mechanics we will try to derive these equations of state from
microscopic models. It is here where we introduce our knowledge of physics. We
might need a classical description of the motion of atoms in a gas, we could have
to use a standard quantum mechanical theory of the motion of electrons in a
crystal, or we might even have to introduce quantum electrodynamics for nuclei
or quarks. Sometimes relativistic effects have to be included. Depending on the
values of the state variables used to define the system different models could be
needed. For example, at room temperature the electrons in some semiconductors
behave like classical particles, but in other semiconductors quantum mechanical
effects are essential.
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