用最优控制优化松弛路径
Optimising the relaxation route with optimal control
摘要：
我们研究非平衡稳态之间的连接时间的最小化。作为本质非平衡系统的一个典型例子，被驱动的颗粒气体。对于与时间无关的驾驶，其放松的自然时间尺度的特点是从经验-放松功能-和理论-最近推导出的经典速度限制-的观点。使用控制理论，我们发现，bang-bang协议-包括两个步骤，以最大可能的驱动值加热和零驱动冷却-最大限度地减少连接时间。砰-砰时间比经验弛豫时间和经典速度极限都要短：在这个意义上，弛豫的自然时标被击败了。信息理论的量来自Fisher信息也分析了这些最佳协议。在颗粒气体动力学的数值模拟中，Bang-Bang过程的实现与理论预测吻合得很好。此外，我们的结果的一般意义进行了讨论，为广泛的一类驱动非平衡系统。具体来说，我们表明，类似的砰砰协议，与一些刘海等于相关的物理变量的数量，在相当一般的条件下，给出了最小的连接时间。
英文摘要：
We look into the minimisation of the connection time between non-equilibrium steady states. As a prototypical example of an intrinsically non-equilibrium system, a driven granular gas is considered. For time-independent driving, its natural time scale for relaxation is characterised from an empirical -- the relaxation function -- and a theoretical -- the recently derived classical speed limits -- point of view. Using control theory, we find that bang-bang protocols -- comprising two steps, heating with the largest possible value of the driving and cooling with zero driving -- minimise the connecting time. The bang-bang time is shorter than both the empirical relaxation time and the classical speed limit: in this sense, the natural time scale for relaxation is beaten. Information theory quantities stemming from the Fisher information are also analysed over these optimal protocols. The implementation of the bang-bang processes in numerical simulations of the dynamics of the granular gas show an excellent agreement with the theoretical predictions. Moreover, general implications of our results are discussed for a wide class of driven non-equilibrium systems. Specifically, we show that analogous bang-bang protocols, with a number of bangs equal to the number of relevant physical variables, give the minimum connecting time under quite general conditions.
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