Elementary Processes and Fluctuations

Abstract

To understand matter on a macroscopic scale, it is necessary to pay attention to its molecular makeup. That is one of the lessons to be learned from the kinetic theory of Maxwell and Boltzmann. Another lesson from kinetic theory is that the dynamical equations, which describe the change of macroscopic systems, have thermodynamics built into them. Indeed, this is the basic content of Boltzmann’s H-theorem. This is also apparent in the Onsager theory which is based on the observation that thermodynamic forces are responsible for the relaxation to equilibrium. In the Onsager theory molecular fluctuations are also related to thermodynamic quantities: The stationary equilibrium fluctuations are determined by the second differential of the entropy, δ²S, and the random noise in the thermodynamic fluxes is determined by the dynamic coupling matrix, L_ij. All this suggests that both thermodynamics and fluctuations are imbedded in a deeper formalism—a formalism which, like the Boltzmann equation, is based on a picture of molecular events.