Unified Theories Of Equilibrium/Nonequilibrium Thermodynamics And Quantum Dissipation For Open Systems

Thermodynamics is a macroscopic phenomenological theory being capable of describing thermal phenomena.Thermodynamics has always been one of the most profound and influential parts of classical physics.Einstein once said that classical thermodynamics is the only physical theory with universal content.How about quantum thermodynamics?In the field of quantum physics,the applicability of the traditional laws of thermodynamics is a issue worth studying.Quantum thermodynamics is an emerging research field,which attempts to investigate whether the macroscale thermodynamics is applicable at the quantum scale,or whether there are new laws at the nanoscale.In this thesis,we study the equilibrium and non-equilibrium thermodynamics of open quantum systems by using dissipaton equation of motion(DEOM)theory.The so-called open system must not be isolated,but interacts with its environment(also called "bath").There may be exchanges of energy,matter,and information between the open system and bath.We call the total system-and-bath composite as the "thermodynamic system".It is in thermal contact with the surrounding reservoir to maintain the constant temperature.In Chapter 1,we introduce the research background and thesis structure,and give additional explanations.In Chapter 2,we review some basic knowledge of quantum statistical mechanics,includes the quantum Liouville equation;Schrodinger picture,Heisenberg picture and Interaction picture;the statistical ensemble of thermodynamic systems and linear response theory.Above provides the foundation for us to carry out theoretical study.In Chapter 3,we introduce the dissipaton equation of motion(DEOM)theory for open quantum systems.On the basis of well-established DEOM,we propose the imaginary-time DEOM(i-DEOM)approach and employ it to investigate equilibrium thermodynamics in Chapter 4.The i-DEOM theory completes the study of open quantum systems’ equilibrium thermodynamics.DEOM theory considers the effect of entanglement system-and-bath properties of complex systems.It is a rigorous theory for studying the dynamics and thermodynamics of open quantum systems.In Chapter 4,on the basis of the thermodynamic integration’s combination with DEOM theory,we presents a unified framework for solving equilibrium and transient thermodynamics,and its evaluations on the Helmholtz free energy change due to the isotherm mixing of two isolated subsystems.A new method is given for calculating equilibrium thermodynamic quantities of open quantum systems.As illustrations,we report the numerical results on a spin-boson system.The difference between thermodynamic entropy and von Neumann entropy,which is often mistaken in open quantum systems,is emphasized.We also compare the imaginary-time(i-DEOM)to the realtime DEOM,the effectiveness of the new method has been clearly verified.In Chapter 5,we develope the free-energy spectrum theory for thermodynamics of open quantum impurity systems that can be either fermionic or bosonic or combined.We complete the system-bath entanglement with fermionic Gaussian coupling environments and show that the system-bath entanglement theory is related to the free-energy spectral functions.We conclude that the thermodynamic hybridizing free-energy can be completely determined with the local impurity system properties and the nonlocal bath hybridization functions.The proposed two types of thermodynamic free energy spectrum functions provide an intuitive and effective theoretical tool for characterizing the thermodynamic properties of measurable quantum impurity systems.In Chapter 6,for the thermodynamic process far from equilibrium in open quantum systems,we investigate the nonequilibrium work distribution in the system-bath isothermal mixing process by using the characteristic function of work(CFW)and defining dissipatons-augmented work operators(DWOs).The celebrated fluctuation theorems of hybridation work,such as the Jarzynski inequality and Crooks relation,which relate equilibrium free energy differences to the work done on thermodynamics system during non-equilibrium process,are verified.It is of great significance to accurately evaluate the non-equilibrium thermodynamic quantities of open systems.In Chapter 7,we employ the hierarchical equation of motion(HEOM)approach to explore the entanglement of a strongly correlated double quantum dots(DQDs)system.Quantum dots comprise a type of quantum impurity system.The entanglement of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with environments.By evaluating various quantities that quantify entanglement,we indicate that the entanglement is mainly determined by the spin-spin correlation.Finally,a brief summary and prospect for the whole thesis is given in Chapter 8.