The thermostatistic properties of a q-generalized boson system trapped in an n-dimensional harmonic oscillator potential are studied, based on the generalized statistic distribution derived from Tsallis' entropy. The density of states, total number of particles, critical temperature at which Bose-Einstein condensation occurs, internal energy, and heat capacity at constant volume are derived. The characteristics of Bose-Einstein condensation of the system are discussed in detail. It is found from the results obtained here that the thermostatistic properties of such a system depend closely on parameter q, dimensional number of the space, and frequency of the harmonic oscillator; and the external potential has a great influence on the thermostatistic properties of the system.

The cycle model of a regenerative quantum heat engine working with many nonineracting harmonic oseillators is established. The cycle consists of two isothermol and two constant-frequency processes. The performance of cycle is investigated, based on the quantum master eqution and semigrop approach. The inherent regenerative losses in the two constant-frequency processes are calculated. The expressions of several important performance paramketers cases. Especially, the optimal performance of the cycle in htgh-temperature limit derived for several intersting cases. Especially, the optimal perfomance of the cycle in higt-temperature limit is discussed in detail. The maximum power output and the corresponding parameters are calculated. The optimal region of the efficiency and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined.

The cycle model of a quantum refrigerator composed of two isothermal and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin- 1 2 systems. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. Especially, the case at high temperatures is analyzed in detail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of the quantum refrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot refrigerator are derived simply.

The thermodynamic properties of a q-generalized ideal boson system with the general energy spectrum ε=aps in a D-dimensional space are investigated, based on the q-generalized statistical distributive function derived by Tsallis entropy. Several important parameters of the system such as the critical temperature tha Bose-Einstein condensation (BEC) occurs, the specifie heat at constant volume, etx. are derived analytically. It is found that the conditions that BEC may occur and the continuity of the specific heat at critical temperature are the same as those of an ordinary boson system. However, the thernodynamic properties of a q-generalized ideal boson system are closely depend on q and D/s and consequently there are some novel results.

The performance of a multi-couple thermoelectric device as a generator is inverstigated. The general expressions of two important performance parameters, the efficeiency and power output, are given. The η-K characteristic curves of a thermoelectric generator are presented for some differently constrained conditions, where η is the efficiency of the thermoelectric system and K is total thermal conductance of the multi-couple thermoelectric device. The mazimum efficeiency of the system if calculated. The structure parameters of the device are optimized. The effect of the thermal conductances between the thermoelectric device and the external heat reservoirs on the performance of the system is expounded by using some representative numerical examples. The results obtained here will be useful for a more detiled investigation and for the optimal design of real thermoelectric generators.