Research On Quantum Thermodynamics Related Issues Under Cascade Mode

The continuous exploration of classical thermodynamic laws in the quantum field has contributed to the rapid development of it.In these explorations,people have attempted to expound the influence of quantum effects on thermodynamic processes,such as how to use quantum coherence and quantum information resources to discover new thermodynamic properties,or improve the performance of thermodynamic devices.On account of the open quantum system as major research object of quantum thermodynamics,the dynamic evolution is generally depicted by the method of quantum master equation.Nevertheless,with the profound exploration of quantum thermodynamics,it is found out that the traditional master equation could lead to thermodynamic inconsistency,thus,the collision model has come to an alternative choice for investigating quantum thermodynamics.The collision model,simulates the environment as a series of ancillas prepared in the same state,and the system reacts with these ancillas in sequence(i.e.,collide).According to the collision model,we have reconstructed the calculation methods of work,heat and other thermodynamic quantities,and come to some meaningful conclusions.We have researched a special collision model,i.e.,cascaded model,which describes the subsystem interacts with the common environment in a cascaded way,namely,S1 interacts with an ancilla first,and then interacts with S2,resulting in a one-way impact between S1 and S2.On one hand,from the perspective on thermodynamic,the cascaded interaction mode doesn’t affect the local heat flow of S1,which is exactly the case in the absence of S2,but on the other hand induces nonlocal heat flow entirely caused by S2.The local and nonlocal components of thermodynamic quantities can be treated independently by using this characteristic of the cascade model.Moreover,the dynamics of the two subsystems are different.The S1 experience Markov dynamics as well as the whole system,while S2 experiences non-Markov dynamics.For this point,we have conducted the following research:Firstly,the general properties of quantum thermodynamics under the cascade model are studied.The general expressions of thermodynamic quantities under the cascaded model are obtained and the forms of nonlocal work and heat generated by the cascaded interactions between the system and ancillas are determined.For a specific system containing two qubits,it is shown that the thermodynamics of S2 will be affected in one direction when the interaction S1-R between S1 and environment R is in a non-conservation of energy form.We show that under the condition of non-conservation of energy,the system will reach a non-equilibrium state maintained by work.In addition,the steady-state coherence generated in the cascaded model is a useful resource from which work can be extracted,which is greatly increased compared to the general non-cascaded model.Secondly,we have carried out research on the asymmetry influence of cascaded model on heat engine.We construct a new model,in which the key part is the cascaded collision form or the common collision form.At the same time,the common collision form has symmetry,so it is set for contrast.After the system evolution equations and thermodynamic quantities of two collision forms derived,the types and purposes of quantum heat engines are analyzed.Among them,we focused our attention on engine and refrigerator.It is found that the cascaded collision mode can optimize the performance of engine and refrigerator by calculating the efficiency and the cooling coefficient.Thirdly,we have studied the Landauer’s principle under the cascaded model.Landauer’s principle can be expressed as an inequality relationship(ΔQ≥ΔS/β)between the entropy reduction(ΔS)in the system and the heat dissipated(ΔQ)to the environment.Although it has been reported that the whole system of the cascaded model meets the Landauer’s principle,there still lacks separate discussion on two subsystems.In the cascade model,although the reduced dynamics of the subsystem S1 are also Markov,the dynamics of S2 depend on S1 and are usually non-Markov,so it is not clear whether the subsystem satisfies Landauer’s principle.We derive the Landauer inequality of the two subsystems in detail,and find S1 satisfies the Landauer’s principle,while S2 violates,and violation conditions are given.