Abstract
Stochastic resonance1,2,3 is often defined as a noise-induced rise (and then fall, for higher noise intensities) of the signal-to-noise ratio (SNR) of a weak narrow-band signal in a nonlinear system. Various applications of this phenomenon are being explored, in particular the possibility that stochastic resonance might help enable biological cells to respond to weak 50-60-Hz electromagnetic fields, far below the thermal noise level4,5. We therefore feel that its place within the broader physics context should be specified more clearly. Specifically, what stochastic resonance can, and cannot, be expected to do.
Main
The idea of stochastic resonance might seem counterintuitive. However, soon after its discovery in bistable systems, it was realized that the idea amounted to a fairly straightforward extension of earlier work by Debye6 on reorienting polar molecules, and that the occurrence of stochastic resonance in the general case could be treated7 with a traditional technique of statistical physics8: linear response theory (LRT). It is well known in the LRT context that the response of a system to signals in certain frequency ranges can be strongly increased by noise, for example by raising the temperature. Examples range from currents in electron tubes to optical absorption near absorption edges in semiconductors. The threshold-less model considered by Bezrukov and Vodyanoy9, the subject of recent discussions4,5, displays noise-induced increases in both the signal and the SNR. Their formula for the SNR represents a special case of the general LRT expression given earlier7 and subsequently applied to many different systems7,10,11,12.
An important consequence10,13 of LRT, relevant to the recent discussion4,5, is that, for a system driven by a signal and Gaussian noise, the SNR at the output, Rout, does not exceed that at the input, Rin. For a linear system Rout = Rin, and the SNR decreases with increasing noise intensity. For a nonlinear system Rout/Rincan be small; then the provision of additional noise can sometimes help to increase the SNR at the output, back towards its value at the input. This latter effect constitutes stochastic resonance. Quite independently of parameter choice4,5, therefore, the SNR of the 50-60-Hz signal inside the biological cell (output signal) cannot be expected to exceed that of the external signal coming from the environment (input signal).
Stochastic resonance can decrease quite markedly the SNR degradation of a noisy signal caused by its transduction through a nonlinear element, but it does not provide a mechanism by which the SNR of the weak input signal can meaningfully be enhanced.
References
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Dykman, M., McClintock, P. What can stochastic resonance do?. Nature 391, 344 (1998). https://doi.org/10.1038/34812
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DOI: https://doi.org/10.1038/34812
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