Agarwal G S, Chaturvedi S
Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078-3072, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012130. doi: 10.1103/PhysRevE.88.012130. Epub 2013 Jul 23.
We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.
我们提出了一种自成体系的形式主义，它以量子谐振子的布朗运动为模型，用于描述微观布朗热机（如卡诺热机、斯特林热机和奥托热机）的性能。我们的理论除了能在稳态下重现标准热力学结果外，还使我们能够研究耗散在实际实验室条件下对布朗热机效率的影响。特别地，我们详细分析了与一个处于平衡态的系统与一个热库解耦并重新耦合到另一个热库相关的动力学过程，并得到了精确的解析结果，这些结果显示出对涉及该步骤的热机效率有重大影响。我们还开发了一种简单而强大的技术，用于计算有限运行时间对稳态结果的修正，并利用它得出各种运行条件下的热力学互补关系，以及计算上述三种热机在最大功率时的效率。这里提出的一些方法和精确可解模型本身就很有趣，并且在其他情况下也可能找到有用的应用。
