论文标题
随机加热发动机的快进方法
Fast forward approach to stochastic heat engine
论文作者
论文摘要
Masuda和Nakamura提出的快进（FF）方案（\ textit {Proc。R.Soc。A} \ TextBf {466}，1135（2010））在保守量子动态的背景下可以在任意短时间内重现准静态动力学。我们将FF方案应用于经典的随机Carnot样热发动机，该发动机由布朗粒子驱动，并与时间相关的谐波电位相结合，并在高（$ t_h $）和低（$ t_c $）和低温（$ t_C $） - 温度温度热储存之间工作。集中于包括动量自由度不足的情况下，我们找到了加速等温和热可绝化过程所需的FF协议的明确表达式，并获得可逆且不可逆转的工作。不可逆转的工作表明，由两个术语组成，一个术语与摩擦系数成正比，另一个与另一个成反比。效率$η$的最佳值$η^*= \ frac {1} {2} {2} {2} \ left（1+ \ frac {1} {2} {2} {2} \ left（\ frac {t_c {t_h} {t_h} {t_h} {t_h} {t_h} { \ frac {5} {4} \ frac {t_c} {t_h} +o \ left（\ left（\ frac {t_c} {t_h} {t_h} \ right）^{\ frac {\ frac {3} \ left（\ frac {t_c} {t_h} \ right）^{\ frac {1} {2}}} $，分别在强大和弱消散的情况下。对于广泛的时间扩展功能，结果是合理的，这使得FF协议非常灵活。我们还透露，在过度阻尼的情况的框架内无法想象类似Carnot的随机热发动机的加速整个周期，并且仅当考虑到动量自由度时，才能评估功率和效率。
The fast-forward (FF) scheme proposed by Masuda and Nakamura (\textit{Proc. R. Soc. A} \textbf{466}, 1135 (2010)) in the context of conservative quantum dynamics can reproduce a quasi-static dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high ($T_h$)- and low ($T_c$)-temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally-adiabatic processes, and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency $η$ at the maximum power of this engine is found to be $η^*=\frac{1}{2} \left( 1+\frac{1}{2}\left(\frac{T_c}{T_h}\right)^{\frac{1}{2}} - \frac{5}{4}\frac{T_c}{T_h} +O\left(\left(\frac{T_c}{T_h}\right)^{\frac{3}{2}}\right)\right)$ and $η^*= 1- \left(\frac{T_c}{T_h}\right)^{\frac{1}{2}}$, respectively in the cases of strong and weak dissipation. The result is justified for a wide family of time scaling functions, making the FF protocols very flexible. We also revealed that the accelerated full cycle of the Carnot-like stochastic heat engine cannot be conceivable within the framework of the overdamped case, and the power and efficiency can be evaluated only when the momentum degree of freedom is taken into consideration.
