The Fluctuations In Irreversible Quantum Otto Cycles

In this thesis,we study fluctuations in finite-time quantum Otto cycles which—include heat engine and its reverse operation,refrigerator.For quantum Otto engines,we focus on the power fluctuations by studying the relation between power fluctuations and thermodynamic efficiency.For quantum Otto refrigerators,we discuss the coefficient of performance and cooling rate,as well as their fluctuations.When referring to numerical calculation,a two-level system recently adopted in experiments is used as the working substance of these quantum thermal machines.In chapter 1,we introduce the irreversibility of finite-time quantum Otto cycles and give a brief description of the research background to establish the relevance of our study.In chapter 2,we discuss the derivation of that the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration.The time-dependent work fluctuations,average work,and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system.The effects of the irreversibility originating from finite-time cycle operation on the thermodynamic efficiency,work fluctuations,and relative power fluctuations are discussed.In chapter 3,we study quantum Otto refrigerators in finite-time cycle period.Finite-time cycle period for a quantum Otto machine implies that either a driving stroke or an isochoric process proceeds in finite time duration.The quantum Otto refrigerators under consideration consist of two driving strokes,where the system(isolated from the heat reservoir)undergoes finite-time unitary transformation,and two isochoric steps,where the system may not reach thermal equilibrium even at the respective ends of the two stages due to finite-time interaction intervals.Using two-time projective measurement method,we find the probability distribution functions of both coefficient of performance and cooling load,which are dependent on the time duration along each process.With these distributions we find the analytical expressions for the performance parameters as well as their fluctuations.We then numerically determine the performance and fluctuations for the refrigerator operating with a two-level system employed in a recent experimental implementation.Our results clarify the role of finite-time durations of four processes on the performance and fluctuations of the quantum Otto refrigerators.Chapter 4 summarizes our main conclusions in the thesis,and gives some interesting issues that may deserve to be studied in future.