Kinetic Derivation of Gauss's Law and Its Thermodynamic Significance*

The entropy S is a dimensionless quant i ty since the tempera ture T has dimensions of energy so that it can be measured in energy units. The r a n d o m variable n is the number of particles, and n s denotes its average or mos t probable value. E is the internal energy, p the chemical potential and V the volume. According to (1), the entropy is the thermodynamic potential tha t determines the error law for which the average value is also the most probable value. In order to determine the entropy, it was necessary to provide a cont inuous time M a r k o v process that admits an invariant p roba bility distr ibution [1]. Casting this s tat ionary distr ibution in the form of (1) identifies the entropy, and subsequent application of the second law (2) gives the