  In this paper, we take a control-theoretic approach to answering some
standard questions in statistical mechanics, and use the results to derive
limitations of classical measurements. A central problem is the relation
between systems which appear macroscopically dissipative but are
microscopically lossless. We show that a linear system is dissipative if, and
only if, it can be approximated by a linear lossless system over arbitrarily
long time intervals. Hence lossless systems are in this sense dense in
dissipative systems. A linear active system can be approximated by a nonlinear
lossless system that is charged with initial energy. As a by-product, we obtain
mechanisms explaining the Onsager relations from time-reversible lossless
approximations, and the fluctuation-dissipation theorem from uncertainty in the
initial state of the lossless system. The results are applied to measurement
devices and are used to quantify limits on the so-called observer effect, also
called back action, which is the impact the measurement device has on the
observed system. In particular, it is shown that deterministic back action can
be compensated by using active elements, whereas stochastic back action is
unavoidable and depends on the temperature of the measurement device.
