Tumbling mills and the theory of large deviations

"Tumbling mills are machine, operating in non-equilibrium, capable of applying forces on the ore contained within, causing the ore to break down. The action of the mill on the ore is very inefficient, producing a large quantity of heat. The inefficiencies of the mill drive the desire for improvement, spawning research and development activities. Given the non-equilibrium nature of the mill, the theory of Large Deviations is proposed as the framework that captures the state of the mill. The theory of Large Deviations allows for the determination of the rate function and the scaled cumulant generating function (SCGF), for systems in either equilibrium or non-equilibrium. Powerful connections can been made between familiar concepts of statistical physics and the concepts introduced by the theory of Large Deviations: entropy can be associated with the rate function; the scaled cumulant generating function with the free energy. It is shown that observables, compatible with Large Deviation theory, can be identified for the tumbling mill. Here, the time series of the energy associated with an element of the charge is such an observable. Furthermore, using some experimental data, it is shown that the time series of the energy can define a rate function, thereby describing the system within the Large Deviation framework. Finally, a discussion of the results is given, particularly how this theory can be further developed for tumbling mills."