On the existence of Gaussian noise [signal modelling]

It is noted that the dependence structure and the amplitude distribution of stationary random sequences are linked, with specification of one placing constraints on the other. Time-reversible processes can be Gaussian or non-Gaussian, but all Gaussian processes must be time reversible. The authors examine the thermodynamics of measurements, showing that while information can be extracted from a system without altering system entropy, most measurement techniques irreversibly alter the thermodynamic state with a consequent entropy increase. Because of the second law of thermodynamics, such entropy changes cannot be undone and measurements reflecting thermodynamic state cannot be time reversible. It is concluded that physical measurements are not time reversible, implying that only non-time-reversible processes model physically relevant signals. Consequently, Gaussian processes would seem to be imprecise representations of physical measurements