LOG-NORMAL DISTRIBUTIONS OF THE CHARACTERISTICS OF NATURAL SYSTEMS AS AN EXPRESSION OF THE SECOND LAW OF THERMODYNAMICS

Abstract

According to the Second Law of Thermodynamics, 'natural processes tend from less probable to more probable states,' and we use the entropy of a system as a measure of the thermodynamic probability P of its state. For this entropy Boltzmann gives an equation. An equation for entropy is given that relating the entropy of the system, the Boltzmann constant, and a constant of integration. The model value of the theoretical plot of this equation may be interpreted, in terms of statistical physics, as the most probable state of the system. The presence of a rightward skewness of the log-normal probability density distribution indicates that at a given distance from the mode, the number of probable microstates of the system is greater on the right side than on the left side. This conclusion is consistent with the thermodynamic character of entropy, which can only increase in closed systems. Takes account of real geological situations in relatively open (metamorphic) and relatively closed (igneous) systems. The interpretation of the log-normal distributions derived earlier from mathematical modeling acquires a new thermodynamic meaning. This type of curve corresponds to the distributions of the parameters of systems, or their matrices, in which processes proceed in accordance with the Second Law of Thermodynamics. Log-normal distributions are practically everywhere exhibited by certain petrogenic components which may undergo eulysis under specific circumstances. These and other aspects of the subject are discussed.