Weak invariants, temporally-local equilibria, and isoenergetic processes described by the Lindblad equation

The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the Lindblad type that admit time-dependent Hamiltonians as weak invariants. The method for determining the correction presented here may be thought of as a quantum-mechanical analog of the Chapman-Enskog expansion in nonequilibrium classical statistical mechanics. Then, the theory is applied to the time-dependent harmonic oscillator as a simple example, and the power output and the work along an isoenergetic process are evaluated within the framework of finite-time quantum thermodynamics.Comment: 16 pages, no figures. Published versio

Exotic properties and optimal control of quantum heat engine

A quantum heat engine of a specific type is studied. This engine contains a single particle confined in the infinite square well potential with variable width and consists of three processes: the isoenergetic process (which has no classical analogs) as well as the isothermal and adiabatic processes. It is found that the engine possesses exotic properties in its performance. The efficiency takes the maximum value when the expansion ratio of the engine is appropriately set, and, in addition, the lower the temperature is, the higher the maximum efficiency becomes, highlighting aspects of the influence of quantum effects on thermodynamics. A comment is also made on the relevance of this engine to that of Carnot.Comment: 18 pages, 3 figures, 1 table. Published versio

Maximum Power Output of Quantum Heat Engine with Energy Bath

The difference between quantum isoenergetic process and quantum isothermal process comes from the violation of the law of equipartition of energy in the quantum regime. To reveal an important physical meaning of this fact, here we study a special type of quantum heat engine consisting of three processes: isoenergetic, isothermal and adiabatic processes. Therefore, this engine works between the energy and heat baths. Combining two engines of this kind, it is possible to realize the quantum Carnot engine. Furthermore, considering finite velocity of change of the potential shape, here an infinite square well with moving walls, the power output of the engine is discussed. It is found that the efficiency and power output are both closely dependent on the initial and final states of the quantum isothermal process. The performance of the engine cycle is shown to be optimized by control of the occupation probability of the ground state, which is determined by the temperature and the potential width. The relation between the efficiency and power output is also discussed.Comment: 17pages,5figure

Generalized entropies under different probability normalization conditions

National Natural Science Foundation of China [11005041]; Natural Science Foundation of Fujian Province [2010J05007]; Scientific Research Foundation for the Returned Overseas Chinese Scholars; Basic Science Research Foundation of Huaqiao University [JB-SJ1Tsallis entropy and incomplete entropy are proven to have equivalent mathematical structure except for one nonextensive factor q through variable replacements on the basis of their forms. However, employing the Lagrange multiplier method, it is judged that neither yields the q-exponential distributions that have been observed for many physical systems. Consequently, two generalized entropies under complete and incomplete probability normalization conditions are proposed to meet the experimental observations. These two entropic forms are Lesche stable, which means that both vary continuously with probability distribution functions and are thus physically meaningful

Possible canonical distributions for finite systems with nonadditive energy

It is shown that a small system in thermodynamic equilibrium with a finite thermostat can have a q-exponential probability distribution which closely depends on the energy nonextensivity and the particle number of the thermostat. The distribution function will reduce to the exponential one at the thermodynamic limit. However, the nonextensivity of the system should not be neglected.Comment: 13 pages, 4 figure