On Equilibrium Fluctuations

This paper considers a dynamical system described by multidimensional state vector x. A component x of x evolves according to dx/dt = f(x). Equilibrium fluctuations are an equilibrium solution x(t) obtained when the is in its reached under constant external forcing. The frequencies these range from major underlying dynamics lowest possible frequency, frequency zero. For such system, known feature differential operator d(?)/dt as high-pass filter makes spectrum f vanish not only at zero, but de facto over entire centered zero (when considering both positive and negative frequencies). Consequently, there non-zero portion total variance that cannot be determined forcing f. Instead, this arises many impulse-like interactions with other components x, which received along time. effect can realized integrating evolution equations form f(x) forward integral contained in, hence explained by, defined individual time instances.