Canonical ensemble with temperature limitation

摘要

Ideal Bose and Fermi systems are studied on the basis of a canonical ensemble, subject to the condition that their temperature is less than a given temperature T-max. A single new parameter (the tau-parameter, tau) is needed to keep account of the new constraint. The parameter tau is shown to be the exponential of a pseudo-chemical potential that is linearly dependent on temperature. The inclusion of the tau- parameter leads to generalizations of usual thermodynamic quantities (internal energy, heat capacity and entropy) and various particular cases are discussed. The heat capacity of a Bose system can exhibit a maximum at a temperature less than the maximum temperature T-max. The number of micro-states in the canonical ensemble is found to increase with tau. The heat capacity c(v) of a Fermi system of non-interacting spills exhibits a. Schottky anomaly. The peak depends on tau, and for some cases c(v)/k can significantly exceed unity. The influence of tau on the entropy of the Fermi system and on the number of micro-states in the canonical ensemble is significant but not spectacular.