ABSTRACT
Under conditions of high temperature and low density, we shall ˆnd that it does not matter whether classical or quantum mechanical descriptions are used for a system of particles. At high densities and low temperatures this is no longer true, because of the overlap of the particles’ wave functions and quantum mechanics must be used, giving rise to quantum statistics. Under high-density, low-temperature conditions, the properties of a system depend in a crucial way on whether the particles that make up the system are fermions or bosons. Many fascinating phenomena occur in condensed matter as the temperature is lowered. Examples are ferromagnetism, superconductivity, and super…uidity. ese important new properties appear fairly abruptly at phase transitions. Progress in the microscopic understanding and description of the behavior of these systems involves quantum mechanics and statistical physics ideas. Applications of quantum statistics are not conˆned to terrestrial systems and include astrophysical phenomena such as the microwave background radiation from the Big Bang and the mass-radius relationships for white dwarf stars and neutron stars. An important concept in thermal physics is that of entropy, which, as we shall see, increases with time as systems become more disordered. e increase of the entropy of the universe with the passage of time provides what is termed time’s arrow. An interesting and unanswered question arises as to why the entropy of the universe was so low at the beginning of time.
