On the Regression of Fluctuations

Both the formal and molecular aspects of fluctuation theory are considered with the aim of computing transport coefficients. The formal theory of the regression of fluctuations is presented from the standpoint of least-square linear prediction theory. Thereby the transport coefficients are expressed in terms of correlations between fluctuations and time averaged fluxes. The necessary dynamics is developed with the assumption that the potential energy of interaction between a small group of molecules and the rest of the system decays only slightly during the minimum time interval required to establish the flow processes. The theory is briefly illustrated with an application to diffusion.