On the basis of the probability distribution of the various values of the fluctuation and the fundamental equation of thermodynamics of any given system, a simple and useful method of calculating the fluctuations is presented. By using the method, the fluctuations of thermodynamic quantities can be directly determined from the fundamental equation of thermodynamics. Finally, some examples are given to illustrate the use of the method.

A thermodynamic model including four irreversiblilities is used to investigate the optimal Performance a solar-driven thermoelectric generator. The efficiency of the system is derived and taken as and objective function for optimiztion. Some important curves, such as the efficiency of the system versus the operating temperature of the solar collector, the reduced current, and the load resistance, are obtained. These curves can reveal the performance charaterisistics of solar-driven thermoelectric generators. the maximum efficeiency of the system and the corresponding reduced current are derived for some special cases. The optimal matching of load resistance which is one of the kdy problems in the optimal design of solar-driven thermoelectric generators is discussed. New bounds of the key performance parameters, such as the efficiency, power output, and load resistance, are determined.

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 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.

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.