The Nonequilibrium Thermodynamics of Small Systems

S systems found throughout physics, chemistry, and biology manifest striking properties as a result of their tiny dimensions. Examples of such systems include magnetic domains in ferromagnets, which are typically smaller than 300 nm; quantum dots and biological molecular machines that range in size from 2 to 100 nm; and solidlike clusters that are important in the relaxation of glassy systems and whose dimensions are a few nanometers. Scientists nowadays are interested in understanding the properties of such small systems. For example, they are beginning to investigate the dynamics of the biological motors responsible for converting chemical energy into useful work in the cell (see the article by Terence Strick, JeanFrançois Allemand, Vincent Croquette, and David Bensimon, PHYSICS TODAY October 2001, page 46). Those motors operate away from equilibrium, dissipate energy continuously, and make transitions between steady states. Until the early 1990s, researchers had lacked experimental methods to investigate such properties of small systems as how they exchange heat and work with their environments. The development of modern techniques of microscopic manipulation has changed the experimental situation. In parallel, during the past decade, theorists have developed several results collectively known as fluctuation theorems (FTs), some of which have been experimentally tested. The much-improved experimental access to the energy fluctuations of small systems and the formulation of the principles that govern both energy exchanges and their statistical excursions are starting to shed light on the unique properties of microscopic systems. Ultimately, the knowledge physicists are gaining with their new experimental and theoretical tools may serve as the basis for a theory of the nonequilibrium thermodynamics of small systems.