The heat and work of quantum thermodynamic processes with quantum coherence

Abstract

Energy is often partitioned into heat and work by two independent paths corresponding to the change in the eigenenergies or the probability distributions of a quantum system. The discrepancies of the heat and work for various quantum thermodynamic processes have not been well characterized in literature. Here we show how the work in quantum machines is differentially related to isochoric, isothermal, and adiabatic processes. We prove that the energy exchanges during the quantum isochoric and isothermal processes are simply depending on the change in the eigenenergies or the probability distributions. However, for a time-dependent system in a non-adiabatic quantum evolution, the transitions between the different quantum states representing the quantum coherence can affect the essential thermodynamic properties, and thus the general definitions of the heat and work should be clarified with respect to the microscopic generic time-dependent system. By integrating the coherence effects in the exactly-solvable dynamics of quantum-spin precession, the internal energy is rigorously transferred as the work in the thermodynamic adiabatic process. The present study demonstrates that quantum adiabatic process is sufficient but not necessary for thermodynamic adiabatic process.

Effect of Finite-Size Heat Source’s Heat Capacity on the Efficiency of Heat Engine

“…Since the last century, with the maturity of quantum theory and its related technologies, people started to pay attention to the performance of quantum heat engines working in micro-scale within the framework of quantum thermodynamics [ 4 , 5 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. Series of the quantum effect, such as coherence, entanglement, quantum phase transition, etc., of the working substance or heat source have been studied to realize better heat engines [ 13 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. On the other hand, with the development of non-equilibrium thermodynamics [ 2 , 3 , 28 ], the optimization of actual heat engines under the framework of finite-time thermodynamics attracted a wide range of attention [ 29 , 30 , 31 , 32 , 33 ].…”

Boosting the performance of quantum Otto heat engines

“…We consider the situation where the time consuming of the finite-time isochoric pro- * hdong@gscaep.ac.cn cesses can be neglected compared to the finite-time adiabatic processes [47,50]. During the finite-time adiabatic process, the system is isolated from the environment and evolves under the time-dependent Hamiltonian [51]. When energy levels of different states do not cross, the quantum adiabatic approximation is valid for long control time [24].…”

Simulating Finite-Time Isothermal Processes with Superconducting Quantum Circuits

“…Yet, simulation of a tuned open quantum system remains a challenge mainly due to the inability to physically tune the control parameters and the difficulty to measure the work extraction. In quantum thermodynamics, the work extraction, as a fundamental quantity [ 28 , 29 , 30 ], requires the tuning of the control parameters. Such requirement is achievable in the specifically designed system, e.g., the laser-induced force on the trapped ion [ 11 ], the trapped frequency of the Fermi gas [ 13 , 14 ], and the external field in the superconducting system [ 15 , 16 ].…”