Statistical mechanics is the theory with which we analyze the behavior of natural or spontaneous fluctuations. It is also true that it is the very nature of these fluctuations that continuously drives all things toward ever increasing chaos. Statistical mechanics and its macroscopic counterpart, thermodynamics, form the mathematical theory with which we can understand the magnitudes and time scales of these fluctuations.
The presence of fluctuations is a consequence of the complexity of the climate system. The macroscopic climate system is composed of so many elementary particles that it is impossible to completely control the system to an extent that would prescribe the evolution of the system in a deterministic fashion. Ignorance, therefore, is a law of nature for the climate system.
Theoretical meteorology has always attempted to be almost completely deterministic in the sense that statistical considerations have been thought of "only to remedy our shortcoming, ignorance of details, or our inability to cope with vast observational material" to quote Schrödinger , (Nature,1944).
It has been said that the success of stochastic methods in physics has been only on microscale phenomena whereas the climate system is in macroscale. This, of course, is a misunderstanding about the size of populations involved. Actually in both cases the population sets are at least denumerable infinite. Schrödinger introduces the statistical law in nature as the law of big numbers and confirms that statistical methods have entered one branch of science after another, including meteorology.
The observed natural spontaneous random fluctuations prevent an exact measurement of the initial state of the climate system. According to the basis of statistical mechanics two nearby initial states will separate exponentially in time. As we do not know the initial state exactly, predictions of future specific states of the climate is not possible.