A frequency- domain inequality for stochastic power flow in linear networks

This paper addresses the frequency-domain characterization of stochastic signals in linear time-invariant distributed networks. A new general relation is derived. The average power flow at each frequency from one source to another through a lossless coupling network is shown to obey an inequality related to the second law of thermodynamics. The sources can be essentially any stationary random signal or noise processes; in particular, they need not represent thermal noise. In this sense the inequality is quite general. Proofs are based on standard techniques from the theory of linear circuits and random signals: thermodynamic concepts are used only for motivation and interpretation.