Department of Physics, Beijing Normal University, Beijing 100875, China.
Zun Yi Si Zhong, Zunyi 563000, China.
Phys Rev E. 2022 Dec;106(6-1):064117. doi: 10.1103/PhysRevE.106.064117.
We construct a microscopic model of low-dissipation engines by driving a Brownian particle in a time-dependent harmonic potential. Shortcuts to adiabaticity and shortcuts to isothermality are introduced to realize the adiabatic and isothermal branches in a thermodynamic cycle, respectively. We derive an analytical formula of the efficiency at maximum power with explicit expressions of dissipation coefficients under the optimized protocols. When the relative temperature difference between the two baths in the cycle is insignificant, this expression satisfies the universal law of efficiency at maximum power up to the quadratic term of the Carnot efficiency. For large relative temperature differences, the efficiency at maximum power tends to be 1/2. Furthermore, we analyze the issue of power at any given efficiency for general low-dissipation engines and then obtain the supremum of the power in three limiting cases, respectively. These expressions of maximum power at given efficiency provide the optimal relations between power and efficiency which are tighter than the results in previous references.
我们通过在时变谐和势中驱动布朗粒子来构建低耗散引擎的微观模型。分别引入绝热捷径和等温捷径，以在热力学循环中实现绝热和等温分支。我们推导出最大功率效率的解析公式，并在优化协议下给出耗散系数的显式表达式。当循环中两个热浴之间的相对温差较小时，此表达式在卡诺效率的二次项内满足最大功率效率的普遍规律。对于较大的相对温差，最大功率效率趋于 1/2。此外，我们分析了一般低耗散引擎在任意给定效率下的功率问题，然后分别在三个极限情况下得到了功率的最大值。这些在给定效率下的最大功率表达式提供了功率与效率之间的最优关系，比以前的参考文献中的结果更为紧密。
