# Fluctuation-Enhanced Sensing (FES): A Promising Sensing Technique
## 2 Fluctuation Enhanced Sensing: A Powerful Sensing Technique  
The conception and development of the fluctuation-enhanced sensing (FES) [32] stems from the observation that, even in the field of sensing, the microscopic, random fluctuation phenomena in physical systems are rich sources of information. Physical and chemical sensing techniques usually involve the measurement of the value of a physical quantity in the detector/sensor. FES was first proposed and developed for chemical and gas sensing and, unlike traditional sensing methods, it takes advantage of the fact the sensed agent changes the statistics of the neural output (a pulse noise) thus acting in a way completely analogous to biological sensing. It is important to underline that in FES it is the noise that carries the sensory useful information. Note that in the past, FES has been used for the measurement of some physical quantities, but the knowledge and technologies available made the application of the technique somewhat complicated. For example, by measuring Johnson noise voltage of resistors it is possible to estimate the temperature [33]. Figure 1 shows the principle on which the usual Johnson voltage noise thermometry is based (Figure 1b), compared with classical resistor thermometry (Figure 1a) and with the application of FES (Figure 1b and 1c combined together). To measure the temperature with a classic resistor, the law of variation of the resistance with temperature \(R(T)\) must be known and, furthermore, to measure the actual value of the resistance a DC bias current is required. This current, however, heats up the resistor thus causing errors in the measurement of \(T\). Although for the conventional Johnson-noise thermometry the \(R(T)\) function is not needed, the problem of measuring the resistance value \(R\) still exists, unless its value is independent of the temperature. However, if the measurement of the voltage noise (b) and of the current noise (c) are combined, we can obtain absolute thermometry based on Johnson noise and first principles and this can be regarded as evidence of the power of FES. Indeed, when both Johnson voltage noise and current noise are measured, we obtain two separate equations. The solution of such a system allows to derive both the absolute temperature \(T\) and the resistance \(R\):  
\[T=\frac{\sqrt{S_{u}S_{i}}}{4k}\;R=\sqrt{\frac{S_{u}}{S_{i}}} \tag{1}\]  
In Equation (1) \(S_{u}\) and \(S_{i}\) are the power spectral densities (PSD) of the voltage and current fluctuations, respectively, and \(k\) is the Boltzmann constant. Compared to the other measurement methods, it must be stressed that in this case no heating occurs and only precise current and voltage measurements are needed. This consideration also indicates that FES, regardless of its simplicity or cheapness, is a very powerful tool. In this paper we want to focus on fluctuation-enhanced sensing of gases and odors, being a topic of great current interest for the control of environments and therefore for the protection of health. To understand the principle and the reason for resorting to FES as gas sensing technique, let us start from the observation that classical gas sensing methods are many orders of magnitude less sensitive than the best gas sensing systems we have in nature: dog noses (or even that of humans). It is therefore fundamental, as a first step, to understand how biological noses work. The operating principle of biological noses is shown in Figure 2. They contain a large array of olfactory neurons that communicate stochastic voltage spikes to the brain. When odor molecules are adsorbed by a quantity of neurons,  
Figure 1: (**a**) Resistor thermometer; the \(R(T)\) function and \(R\) value must be known and a biasing DC current \(I\) that, by unavoidably heating the thermometer causes error, is needed; (**b**) the usual Johnson-noise thermometry: \(S_{U}\) is the power spectral density of the voltage fluctuations across the resistor, \(k\) is the Boltzmann constant, and \(T\) is the absolute temperature.