Comment on “Critical analysis of negative heat capacities in nanoclusters” by Michaelian K. and Santamaría-Holek I.

Contrary to the claims in a recent letter by Michaelianand Santamar´ia-Holek (MSH) [1], heat capacities can benegative in atomic clusters. This effect has been care-fully examined many times in the past [2–7]. Negativeheat capacities can be found in noncanonical ensembles,and have been extensively investigated in microcanoni-cal ensembles, whereas they are always positive in thecanonical ensemble. The finite size of the system is a suffi-cient condition for statistical ensembles to be inequivalent.This inequivalence has also been proved for systems in thethermodynamic limit [8], providing various examples withan “S-bend” in the caloric curve. The Gibbs equationinvoked by MSH does not hold in the microcanonicalensemble.On the other hand, both true non-ergodicity andthe failure to achieve ergodicity due to a finite obser-vation time may also cause S-bends in caloric curves.Intermediate states with the solid and liquid phases incontact can be thermodynamically unfavourable becauseof the free-energy cost of introducing the interface [5].The related energy barriers between the phases increasewith system size. In macroscopic systems they maybecome too high to overcome on the experimental timescale, leading to phase separation, superheating, andsupercooling. Various models have been constructed