The Performance Analysis Of The Quantum Thermodynamic Cycle Using Spin Systems And Harmonic Systems As Working Substance

Quantum thermodynamics is a new hotspot of the modern thermodynamics. Corresponding to classical thermodynamic cycle, quantum Brayton cycle, quantum Otto cycle, quantum Carnot cycle, quantum Ericsson cycle, etc, are intensively studied. The working substance of those cycles may be quantum gas, spin systems, harmonic oscillators systems, two level or multi-level systems. The equation of motion for the working medium system obeys Heisenberg master equation, Pauli master equation. There are many approaches to deal with those cycles, such as, semi-group approach, thermodynamic observables evolution approach, etc. The purpose are try to get some important performance parameters, like the coefficient of performance, cooling rate, and power input or power output, thermodynamic economic function, thermodynamic ecologic function, etc, then ,we can do the optimization of those parameters.In chapterⅠ, the production, development and the present states of quantum thermodynamics are discussed briefly.In chapterⅡ, performance analysis of quantum Brayton heat engine cycle with spin systems as the working substance. A new model of a heat engine cycle is established in which the working substance consists of many non-interacting spin-1/2 systems. The performance characteristics of the cycle and time evolution of the spin angular momentum are investigated, based on the quantum master equation and semi-group approach .The general expression of the efficiency and power output are derived .Further, at high temperatures the optimal relations of the efficiency and power output are researched in detail.In chapterⅢ, performance analysis of quantum Otto refrigeration cycle with harmonic systems. First of all, the set of thermodynamic observables {(H|^),(L|^),(D|^)} for harmonic systems are established. They are the Hamiltonian operator, the Lagrangian operator, and the position-momentum correlation operator, respectively. Based on Heisenberg master equation, we get the evolution differential equations of the set of thermodynamic observables. For quasis-adiabatic condition, the analytic solutions are given. Assume in ideal quasis-adiabatic condition, several important performance parameters, like coefficient of performance, cooling rate, and power input are obtained. Beside, the optimal time allocations in each branch are also calculated. We get the optimum cooling rate. The relationship between optimum cooling rate and compression ratio (C =ω_h/ω_c) or coefficient of performanceεis analyzed. In general case, the evolutionary rules of thermodynamic observables and performance parameters are numerically analyzed by using the former set's evolution differential equations. No matter where is cycle's starting point, it will settle down to a smooth mode of operation determined by the control parameters (like heat or cold bath, high or low frequency, each branch's time). All the performance parameters appear vibration under the influence of quantum friction work.