文档介绍：Statistical mechanics: A selective review of two central issues
Joel L. Lebowitz*
Departments of Mathematics and Physics, Rutgers, The State University of New Jersey,
Piscataway, New Jersey 08854-8019
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of
the time-asymmetric evolution of macroscopic systems towards equilibrium and of first-order phase
transitions in equilibrium. These phenomena are emergent collective properties not discernible in the
behavior of individual atoms. They are given precise and elegant mathematical formulations when the
ratio between macroscopic and microscopic scales es very large. [S0034-6861(99)03402-9]
I. INTRODUCTION ditive effects of the actions of individual atoms, ., the
pressure exerted by a gas on the walls of its container,
Nature has a hierarchical structure, with time, length, while others are paradigms of emergent behavior, hav-
and energy scales ranging from the submicroscopic to ing no direct counterpart in the properties or dynamics
the supergalactic. Surprisingly, it is possible, and in of individual atoms. Particularly fascinating and impor-
many cases essential, to discuss these levels tant examples of such emergent phenomena are the ir-
independently—quarks are irrelevant for understanding reversible approach to equilibrium and phase transitions
protein folding and atoms are a distraction when study- in equilibrium. Both of these would (or should) be as-
ing ocean currents. Nevertheless, it is a central lesson of tonishing if they were not so familiar. Their microscopic
science, very essful in the past three-hundred years, derivation and analysis forms the core of statistical me-
that there are no new fundamental laws, only new phe- chanics. I will discuss the first of these in Sec. II and the
nomena, as one goes up the hierarchy. Thus arrows of second in Sec. III.
explanations between different levels always point from For a more gene