2
1 Basic Background Material
(a) Classical mechanics. If we are to use classical mechanics, we must assume that
we are able to state in some manner the values of the position coordinates x, y, z
and momentum components p x , p y , p z , plus any other relevant dynamical
variables for each atom or molecule in the physical system. Each such set of
values then constitutes what we shall refer to as a classical microstate of the
system under consideration.
(b) Quantum mechanics. If we are to use quantum mechanics, we must be able
to specify the wave (or state) function ψ α (x, y, z, . . .) for each atom or
molecule in the system, including the attendant quantum numbers, which we
have represented collectively by the subscript α on ψ. Each such set of wave
functions we shall refer to as a quantum microstate of the system under
consideration.
Of course it is appealing to attempt to explain or interpret macroscopic behaviour
in terms of laws governing the individual microscopic constituents of the system,
provided that we are able in some way to work out the detailed behaviour of so
many particles. For a typical macroscopic amount, which may consist of a mole of
particles, the fundamental question is, ‘How do we deal with 10 23 or so particles
in interaction?’. Indeed, the problem is intractable from such a point of view, and
so we are in need of a new branch of physics. We shall still require the laws of
mechanics (quantum or classical) and electromagnetism, since they are concerned
with motions and properties of atoms and molecules and with radiation. However,
when we relinquish the idea of arriving at a detailed description of the particle
motions, we need to invent new concepts that are capable of answering the types
of questions that we wish to ask, questions such as:
(1) What is entropy, and why does it always increase in spontaneous processes?
(2) What is the absolute entropy of a given chemical system?
(3) Can the equilibrium constant for a chemical reaction be predicted from a
knowledge of the properties of the individual reactants and products?
(4) How do biological systems work?
(5) How can we understand liquefaction?
To answer such questions as these, the concepts that we must invent should be
extremely powerful. In all likelihood, such powerful concepts will pose a certain
intellectual challenge. Fortunately, however, we shall not require much advanced
mathematics! Indeed, much of the developmental work was carried out more than a
century ago by the founding fathers of the subject, James Clerk Maxwell, Ludwig
Boltzmann, and Josiah Willard Gibbs.
The objective of our study is then to describe the properties of matter—gases,
liquids, solids, plasmas, and polymers—from a microscopic point of view, i.e., by
maximizing the use of the laws of mechanics and electromagnetism. We should
compare this aim with that of thermodynamics and fluid mechanics, in which
matter is described solely in macroscopic terms (without invoking any knowledge
of its molecular structure). In general, such a goal would involve the entire field
of Equilibrium and Nonequilibrium Statistical Mechanics, and this would clearly
1 Basic Background Material
(a) Classical mechanics. If we are to use classical mechanics, we must assume that
we are able to state in some manner the values of the position coordinates x, y, z
and momentum components p x , p y , p z , plus any other relevant dynamical
variables for each atom or molecule in the physical system. Each such set of
values then constitutes what we shall refer to as a classical microstate of the
system under consideration.
(b) Quantum mechanics. If we are to use quantum mechanics, we must be able
to specify the wave (or state) function ψ α (x, y, z, . . .) for each atom or
molecule in the system, including the attendant quantum numbers, which we
have represented collectively by the subscript α on ψ. Each such set of wave
functions we shall refer to as a quantum microstate of the system under
consideration.
Of course it is appealing to attempt to explain or interpret macroscopic behaviour
in terms of laws governing the individual microscopic constituents of the system,
provided that we are able in some way to work out the detailed behaviour of so
many particles. For a typical macroscopic amount, which may consist of a mole of
particles, the fundamental question is, ‘How do we deal with 10 23 or so particles
in interaction?’. Indeed, the problem is intractable from such a point of view, and
so we are in need of a new branch of physics. We shall still require the laws of
mechanics (quantum or classical) and electromagnetism, since they are concerned
with motions and properties of atoms and molecules and with radiation. However,
when we relinquish the idea of arriving at a detailed description of the particle
motions, we need to invent new concepts that are capable of answering the types
of questions that we wish to ask, questions such as:
(1) What is entropy, and why does it always increase in spontaneous processes?
(2) What is the absolute entropy of a given chemical system?
(3) Can the equilibrium constant for a chemical reaction be predicted from a
knowledge of the properties of the individual reactants and products?
(4) How do biological systems work?
(5) How can we understand liquefaction?
To answer such questions as these, the concepts that we must invent should be
extremely powerful. In all likelihood, such powerful concepts will pose a certain
intellectual challenge. Fortunately, however, we shall not require much advanced
mathematics! Indeed, much of the developmental work was carried out more than a
century ago by the founding fathers of the subject, James Clerk Maxwell, Ludwig
Boltzmann, and Josiah Willard Gibbs.
The objective of our study is then to describe the properties of matter—gases,
liquids, solids, plasmas, and polymers—from a microscopic point of view, i.e., by
maximizing the use of the laws of mechanics and electromagnetism. We should
compare this aim with that of thermodynamics and fluid mechanics, in which
matter is described solely in macroscopic terms (without invoking any knowledge
of its molecular structure). In general, such a goal would involve the entire field
of Equilibrium and Nonequilibrium Statistical Mechanics, and this would clearly