Abstract
Explicit formulae for correlation functions and fluctuation spectra of the irreducible three-state Markov processes are presented. The necessary and sufficient conditions of existing nonmonotonic fluctuation spectra on [0, +∞) with respect to real functions are given, which reveals that the nonequilibrium flux must be strong enough to produce a peak in the fluctuation spectrum and the monotonicity of fluctuation spectra is related to the time scales of Markov processes.
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