Quantum effects on thermodynamics of Otto cycle

Abstract

Quantum thermodynamics is the study that investigates quantum systems interacting with the environment. The most important goals of quantum thermodynamics are finding physics laws and understanding the effect of quantum on thermodynamics. To find an answer to "how does quantum affect thermodynamics", we compare several finite-time Otto cycles and analyze the quantum effect on the heat devices. First, we investigate how the structure of the Lindblad bath affects an Otto cycle. The Otto cycle is a simple model that consists of two isochoric processes and two adiabatic processes, so that the finite-time Otto cycle can be solved and an appropriate model to study the role of coherence. The Lindblad bath has a special structure that cannot find in the classical heat bath because it is demanded to assure the positiveness of the density matrix for any Hamiltonian. To study the special structure of the Lindblad bath, we compare an Otto cycle with the Lindblad bath with an Otto cycle with an Agarwal bath that does not have the special structure. From the comparison of cycle performance, we find that the Lindblad Otto cycle stably produces work even in the short-time limit but the Agarwal Otto cycle does not. Moreover, we find counter-intuitive phenomena that quantum friction, which harms the performance of the Lindblad Otto cycle, makes the Agarwal Otto cycle exceed the quasistatic efficiency in the finite-time mode. Finally, to reveal the effects of quantumness, such as Boson statistics and uncertainty principle, we compare the Lindblad with classical Otto cycle. From the exactly calculated the mean values and fluctuations of various thermodynamic quantities, we measure the reliability and productivity of the two Otto cycles. In the quasistatic limit, the Lindblad Otto cycle is less productive and less reliable than that in the absence of quantumness. However, in the finite-time limit, quantumness can improve both the productivity and the reliability. Counterintuitively, as the strength (heat conductance) between the system and the bath increases, we get different results from the quasistatic results. With the high enough heat conductance, the reliability of the Lindblad Otto cycle surpasses that of the classical one. In addition, we test the validity of thermodynamic uncertainty relation (TUR) in the Otto cycles. In the region where the entropy production is large enough and in the quasistatic limit, we find a tighter bound than that of the conventional TUR, and also that the TUR of the Otto cycle in this limit is still valid. However, in the finite-time mode, we find both Lindblad and classical Otto cycles violate the conventional TUR in the region where the entropy production is small. To understand our findings, we discuss the possible origin of the violations from the uncertainty products and relative errors near resonance conditions, which implies that another modified TUR is needed to cover the finite-time Otto cycle.