Fluctuations and Nonequilibrium Processes
摘要
The study of fluctuations is usually relegated to the end of a study of thermodynamics. That creates the impression that it is an advanced subject, not required for a basic understanding of the equilibrium state. On the contrary, it is not possible even to understand temperature without invoking fluctuations, under the guise of Carnot engines. Nevertheless, the impression persisted long after Carnot that equilibrium and nonequilibrium phenomena were somehow fundamentally different, so that when Kamerlingh Onnes discovered superconductivity in 1911, his claim that it was a new phase of matter was contested on the grounds that he found the transition in resistivity, hence, not at equilibrium. Today, everyone knows that a transition in a transport coefficient implies a transition in some equilibrium susceptibility, because the two are proportional to each other, the factor of proportionality being the temperature. The reason for that connection is that static and dynamic friction have the same physical origin. This insight is known as the fluctuation-dissipation theorem, whose first version was discovered by Einstein in his analysis of Brownian motion in 1905. It took another half-century to understand the full implications of Einstein’s relation, culminating in the work of Kubo in the 1950s, who developed the first well-founded quantum expressions for transport coefficients. The foundational period of investigations into second-order responses ended with the work of Onsager.