The Studies Of Basic Quantities Of Quantum Thermodynamics And Quantum Heat Machines

Although the quantum thermodynamics and classical thermodynamics are very different,they are related to each other.The development of thermodynamics is just based on the definitions of work,heat and internal energy.In classical thermodynamics,the three laws can be stated as: “ Energy will neither disappear nor be produced;In an isolated system,the entropy will never decrease;The absolute zero temperature is impossible to reach”.In fact both the first and second law of thermodynamics is based on how to distinguish work and heat,thus forming a complete classical thermodynamic system,in order to achieve remarkable achievements in its field.However,in the field of quantum thermodynamics,there are many definitions of work and heat,which hinders the development of quantum thermodynamics and its application.Therefor,the definitions of work and heat become an urgent problem.In this paper I will investigate the definitions of work and heat,through which the Carnot cycle and its efficiency is achieved in a strongly coupled quantum heat engine.I also give a typical example to verify the validity.The studies include:1.Definitions of work and heat:(1)I give two kind definitions of work,which satisfy the different fluctuations theorem,and simultaneously these two kind definitions correspond to two kind internal energy.(2)I show the form of internal energy is determined by the form of the equilibrium state of heat reservoir after thermalization,and also give the relationship between two internal energy.(3)Through the heat definition,the entropy production can be expressed as relative entropy,which in turn demonstrate that the corresponding heat satisfy the second law of thermodynamics.2.For the Carnot cycle under strong coupled heat engine:(1)Generally the efficiency of a heat engine strongly coupled with a heat bath is less than the classical Carnot efficiency.Through a model-independent method in this paper,the classical Carnot efficiency is achieved in a strongly coupled quantum heat engine.(2)Though relative entropy,two restrictions to realize Carnot cycle isobtained in strongly coupled quantum heat engine.(3)The conclusion is demonstrated with a two-level system in which a work substance strongly interacts with a heat bath.