CONICET | Buscador de Institutos y Recursos Humanos

The statistical mechanics of small clusters (n~10-50 elements) of harmonicoscillators and two-level systems is studied exactly, following themicrocanonical, canonical and grand canonical formalisms. For clusters withseveral hundred particles, the results from the three formalisms coincide withthose found in the thermodynamic limit. However, for clusters formed by a fewtens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators,when the heat capacity per oscillator is evaluated within the canonicalformalism, it reaches a limit value equal to kB, as in the thermodynamic case, while within themicrocanonical formalism the limit value is kB(1 ? 1/n). This difference could be measured experimentally.For a cluster with a few tens of two-level systems, the heat capacity evaluatedwithin the canonical and microcanonical ensembles also presents differencesthat could be detected experimentally.Both the microcanonical and grand canonical formalismshow that the entropy is non-additive for systems this small, while thecanonical ensemble reaches the opposite conclusion. These results suggest thatthe microcanonical ensemble is the most appropriate for dealing with systemswith tens of particles.