布朗回转器的工程快速平衡
Engineered Swift Equilibration of a Brownian Gyrator
摘要：
在随机热力学的背景下，最近提出了一种非平衡定态的极小模型：布朗回转器（BG）。它描述了随机过阻尼运动的粒子在二维谐波势，在经典的Ornstein-Uhlenbeck过程，但考虑同时存在两个独立的热浴。当两个浴具有不同的温度时，稳定的BG表现出旋转电流，这是非平衡动力学的明显特征。在这里，我们考虑一个随时间变化的潜力，我们应用逆向工程的方法来获得所需的协议，从一个初始的稳定状态切换到一个最终的稳定状态在有限的时间$τ$。该协议可以通过首先选择一个任意的准静态对应-很少的约束-然后添加一个有限时间的贡献，它只取决于所选择的准静态形式，其顺序为$1/τ$。我们还得到了一个条件的转换-在有限的时间-保存内能，有用的应用程序，如设计的微观热机。我们的研究将有限时间随机热力学扩展到连接非平衡稳态的变换。
英文摘要：
In the context of stochastic thermodynamics, a minimal model for non equilibrium steady states has been recently proposed: the Brownian Gyrator (BG). It describes the stochastic overdamped motion of a particle in a two dimensional harmonic potential, as in the classic Ornstein-Uhlenbeck process, but considering the simultaneous presence of two independent thermal baths. When the two baths have different temperatures, the steady BG exhibits a rotating current, a clear signature of non equilibrium dynamics. Here, we consider a time-dependent potential, and we apply a reverse-engineering approach to derive exactly the required protocol to switch from an initial steady state to a final steady state in a finite time $τ$. The protocol can be built by first choosing an arbitrary quasi-static counterpart - with few constraints - and then adding a finite-time contribution which only depends upon the chosen quasi-static form and which is of order $1/τ$. We also get a condition for transformations which - in finite time - conserve internal energy, useful for applications such as the design of microscopic thermal engines. Our study extends finite-time stochastic thermodynamics to transformations connecting non-equilibrium steady states.
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