The Tsallis Entropic Index q as a Measure of Distance from Thermal Equilibrium in Paramagnetic Spin Lattices

Abstract

For super–systems C + D comprised of combinations of sub–systems C and D which obey Boltzmann thermo–statistics, the entropy S is additive (SC + SD = SC + D) and extensive and the temperature T is intensive. However, because of finite–size effects, the entropy becomes non–additive and non–extensive, and the temperature non–intensive, for very small systems. In such cases, the Tsallis entropic index q quantifies the extent to which the entropy is non–additive and the temperature is non–intensive. In this paper, we use paramagnetic spin lattices (PSLs) as model systems to demonstrate that q is not only a measure of entropic non–extensivity and temperature non–intensivity, but also the extent to which sub–PSL/super–PSL combinations of various sizes deviate from the global thermal equilibrium condition TC = TD = TC + D. Our results demonstrate that q → 1 as global thermal equilibrium is approached regardless of system size, thus indicating that q is an effective measure of distance from equilibrium.