The Statistical Mechanics of Fluctuation-Dissipation and Measurement Back Action

In this paper, we take a control-theoretic approach to answering some standard questions in statistical mechanics. A central problem is the relation between systems which appear macroscopically dissipative but are microscopically lossless. We show that a linear macroscopic system is dissipative if and only if it can be approximated by a linear lossless microscopic system, over arbitrarily long time intervals. As a by-product, we obtain mechanisms explaining Johnson-Nyquist noise as initial uncertainty in the lossless state, as well as measurement back action and a trade-off between process and measurement noise.