# Fluctuation-Enhanced Sensing (FES): A Promising Sensing Technique
## Fundamental FES Resolution Limits  
### On the Sensitivity and Selectivity  
Microscopic fluctuations perturbations require very small energy, so their statistics in a system carry a lot of information about the system itself. On the other hand, while classical sensing techniques use as information a single value obtained as mean value of the sensor signal, in the case of FES the related statistical distribution functions are data arrays, and thus they can contain orders of magnitude more information.  
The underlying physical mechanism behind the enhanced sensitivity is the temporal fluctuations of the agent's or its fragment's concentration at various points of the sensor volume where the sensitivity of the resistivity against the agent is different. This effect generates stochastic fluctuations of the resistance and, hence, of the sensor voltage when it is biased with a DC current. The voltage fluctuations can be extracted (by removing the mean value by AC coupling) and strongly amplified. Sensitivity enhancement by several orders of magnitude was demonstrated by [PERSON] and coworkers [56] in Taguchi sensors and by [PERSON] and coworkers [58] in nanoparticle films.  
Significantly increased selectivity can be expected depending on the type of sensor and types of available FES \"fingerprints\". We define the selectivity enhancement by the factor specifying how many classical sensors a single fluctuation-enhanced sensor can replace. When using power density spectra, the theoretical upper limit of selectivity enhancement is equal to the number of spectral lines that is, typically, about 10,000. However, when the elementary fluctuations are random-telegraph signals (RTSs) the underlying elementary spectra are Lorentzians [73; 74] and the situation is less favorable because their spectra strongly overlap. Consequently, experiments with COTS sensors indicate that the response of spectral lines against agent variations is often not independent. In a simple experimental demonstration with COTS sensors, a selectivity enhancement of six was easily reachable [38]. However, nanosensor implementation may be able to use all the spectral lines more independently. As both the FES signal in macroscopic sensors and the natural conductance fluctuations of the resistive sensors usually show 1/f-like spectra [73; 74], the lower the inherent 1/f noise strength in the sensor the cleaner the sensory signal. An interesting analysis can be made if we suppose that we shrink the sensor size so much that the different agents probe different RTS signals. Then principles for 1/f noise generation [75] indicate that one can resolve at most a few Lorentzian components in a frequency decade. Supposing six decades of frequency, the maximal selectivity enhancement would be around 18, supposing three fluctuators/decade.  
With bispectra [48; 49; 50], the potential for selectivity increase is even greater because bispectra are two-dimensional data arrays. In the case of 10,000 spectral lines, as mentioned above, the theoretical upper limit of selectivity increase is 100 million, but in the Lorentzian fluctuator limit that number is again radically reduced. Bispectra sense only the non-Gaussian part of the sensor signal, and for the utilization of the full advantages of bispectra it seems necessary to build the sensor within the submicron characteristic size range in order to utilize elementary microscopic switching events as non-Gaussian components. Moreover, the sixfold symmetry of the bispectrum function yields a further reduction of information by roughly a factor six. Using the above-mentioned estimation with three Lorentzian fluctuators/decade, over six decades of frequency, the selectivity enhancement would be around 50. It should be noted that this enhancement is independent from the spectral enhancement discussed above because bispectra probe the non-Gaussian components [73].