标题： 黎曼几何最优驱动与热力学长度及其在化学反应网络中的应用 显示英文标题

标题： Riemannian Geometry of Optimal Driving and Thermodynamic Length and its Application to Chemical Reaction Networks

摘要： 已知在最小耗散条件下，由内可逆驱动的系统的轨迹是平衡态空间上的测地线。因此，状态空间配备了由自由能函数的Hessian矩阵给出的黎曼度量，称为Fisher信息度量。然而，迄今为止给出的推导要求系统和驱动热库都处于局部平衡。在本工作中，我们重新推导了化学反应网络的框架，从而将其适用范围扩展到非平衡情况。此外，由于我们的结果是在没有限制性假设的情况下得出的，我们能够讨论之前无法观察到的现象。我们在化学浓度空间上引入了一个合适的加权Fisher信息度量，并表明它能够表征由扩散驱动引起的耗散，且扩散速率常数可以任意。这使我们能够考虑远离平衡的驱动。作为主要结果，我们证明了将稳态流形等距嵌入浓度空间时，在沿流形驱动系统的情况下，该嵌入给出了耗散的一个下界。我们给出了这个界限以及相应测地线的解析表达式，从而能够分析驱动动力学和热力学的贡献。最后，我们详细讨论了其在准稳温稳态中的应用。 显示英文摘要

摘要： It is known that the trajectory of an endoreversibly driven system with minimal dissipation is a geodesic on the equilibrium state space. Thereby, the state space is equipped with the Riemannian metric given by the Hessian of the free energy function, known as Fisher information metric. However, the derivations given until now require both the system and the driving reservoir to be in local equilibrium. In the present work, we rederive the framework for chemical reaction networks and thereby enhance its scope of applicability to the nonequilibrium situation. Moreover, because our results are derived without restrictive assumptions, we are able to discuss phenomena that could not been seen previously. We introduce a suitable weighted Fisher information metric on the space of chemical concentrations and show that it characterizes the dissipation caused by diffusive driving, with arbitrary diffusion rate constants. This allows us to consider driving far from equilibrium. As the main result, we show that the isometric embedding of a steady state manifold into the concentration space yields a lower bound for the dissipation when the system is driven along the manifold. We give an analytic expression for this bound and for the corresponding geodesic, and thereby are able to dissect the contributions from the driving kinetics and from thermodynamics. Finally, we discuss in detail the application to quasi-thermostatic steady states.