Fluctuation phenomena in physics and chemistry an introduction

More than 150 years ago the Scottish botanist Robert Brown discovered the existence of fluctuations when he had studied microscopic living phenomena. However, the physical nature of the motion, which was named after its discoverer, was not known for a long time. As Darwin wrote in 1876 I called on him [Brown] two or three times before the voyage of the Beagle (1831), and on one occasion he asked me to look through a microscope and describe what I saw. This I did, and believe now that it was the marvelous currents of protoplasm in some vegetable cell. I then asked him what I had seen but he answered me, That is my little secret .  

The other class of fluctuation phenomena, well-known since the work of Gibbs (done in 1902, see Gibbs (1948)) and Einstein (1910), is equilibrium fluctuation. The theory of equilibrium (thermostatic) fluctuations considers the equilibrium state as a stationary stochastic process (see, for example, Tisza Quay (1963) and Tisza (1966)). By thermostatic fluctuation theory the statistical character (e.g. the distribution functions and moments derived from it) can be computed. 

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