References

1

J. W. Gibbs, Elementary Principles in Statistical Mechanics, Yale University Press, New Haven, Conn (1902)

2

L. Boltzmann, Lectures in Gas Theory, Leipzig (1896), translated S. G. Brush Lectures in Gas Theory, Berkeley (1964)

3

E. Schrodinger, Statistical Thermodynamics, Cambridge University Press (1952)

4

It is sometimes asserted that -- since no process creates or destroys energy -- the universe as a whole forms an element of a microcanonical ensemble. However, the best current estimate is that the universe is open, in the cosmological sense, and therefore infinite in extent. If the total energy content of the universe be infinite, the assertion that the universe's total energy content is not changed by any process is not significant. The energy content of an infinite universe, being infinite itself, cannot be said not to change. To put it another way, the usual argument (see Chapter ) that eqn. 1 implies eqn. 2 relies on the assumption that if the energy in a part of an isolated system is increased, the energy available for distribution over the remainder of the system must have been reduced. In a finite system, this assumption is an obvious consequence of energy conservation. In an infinite isolated system, increasing the amount of energy in a small part of the system has no effect on the amount of energy available to be distributed over the remainder of the system, so in an infinite system the usual arguments for proceeding from eqn. 1 to eqn. 2 are not valid.