Study On Stability Of Small-scale Thermal Devices

In this thesis,we study the stability of small-scale thermal devices including low-dissipation cyclic refrigerators and quantum Otto heat engines.For a low-dissipation cyclic refrigerator,we show the existence of the steady-state and reveal the influence of internal dissipation on the steady-state stability.For a quantum Otto engine,we derive the expressions for performance(efficiency and work)and work fluctuations,in which the parameter associated with adiabatic deformation of potential is included.In Chapter 1,we recall a low dissipation engine and a quantum Otto heat engine,and also briefly explain the machine stability that indicates the usefulness of the machine practically.This Chapter gives a brief introduction of the physical background associated with our research present here.In Chapter 2,the local stability of a low-dissipation cyclic refrigerator around the maximum figure of merit is investigated.For the machine under consideration,the irreversibility occurs not only from the heat-transfer process but also from adiabatic processes,where we introduce the so-called internal dissipation to describe the latter.We show that the inclusion of internal dissipation does not change the upper and lower bounds of the coefficient of performance at both the maximum figure of merit and at the cooling rate,respectively.Based on the objective functions,we demonstrate the existence of a single steady-state for the refrigerator and clarify the role of internal dissipation on the thermodynamic steady-state stability.Our results show that the internal dissipation hinders the evolution of the cyclic system towards the steady-state,as expected.In Chapter 3,we consider a quantum Otto heat engine consisting of two isochoric and two adiabatic strokes,where both adiabatic expansion and compression are realized by adiabatically changing the shape of the potential.Here,we show that this adiabatic deformation can change the operating mode and improve machine performance by increasing output work and efficiency,even with the advantage of reducing work fluctuations.If the heat engine is operated at maximum power by optimizing the control parameters,the efficiency exhibits a certain general behavior,η~*=η_C2+η_C~28+O(η_C~3).The conclusions are made in Chapter 4,where we list the possible extensions of our work that deserve to be studied in the future.