Bottzmann or Gibbs entropy? Thermostatistics of two models with few particles

E. N. MIRANDA

JOURNAL OF MODERN PHYSICS

SCIENTIFIC RESEARCH PUBLISHING

Año: 2015 vol. 6 p. 1051 - 1057

We study the statistical mechanics of small clusters (N ~ 10-100) for two-level systems and harmonic oscillators. Both Boltzmann?sand Gibbs?s definitions of entropy are used. The properties of the studiedsystems are evaluated numerically but exactly; this means that Stirling?sapproximation was not used in the calculation and that the discrete nature ofenergy was taken into account. Results show that, for the two-level system,using Gibbs entropy prevents temperatures from assuming negative values;however, they reach very high values that are not plausible in physical terms.In the case of harmonic oscillators, there are no significant differences whenusing either definition of entropy. Both systems show that for N = 100 the exact results evaluated withstatistical mechanics coincide with those found in the thermodynamic limit.This suggests that thermodynamics can be applied to systems as small as these.