论文标题
Fokker-Planck方程的几何热力学：信息几何与最佳传输之间的随机热力学联系
Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
论文作者
论文摘要
我们提出了一种非平衡热力学的几何理论，即几何热力学，使用我们最近在非平衡热力学中熵产生速率的差分几何方面的发展。通过对Fokker-Planck方程的随机热力学熵产生速率的几何形式进行重新审查，我们在信息几何学和最佳运输理论方面引入了非平衡热力学的几何框架。我们表明，所提出的几何框架对于获得几种非平衡热力学关系很有用，例如热力学成本和非平衡系统的入口产生速率的最低热力学成本的可观察到最佳的最佳，最佳的最佳方案之间的热力学权衡关系。我们根据概率密度的梯度流动表达与梯度流量表达和信息几何形状之间的关系以及概率密度空间中的梯度流表达与信息几何形状之间的关系以及在路径概率概率密度的空间中最佳传输和信息几何形状之间的关系，从而通过过量的熵产生速率来阐明信息几何形状与最佳传输理论之间的几个随机性 - 热动力学联系。
We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of differential-geometric aspects of entropy production rate in non-equilibrium thermodynamics. By revisiting our recent results on geometrical aspects of entropy production rate in stochastic thermodynamics for the Fokker-Planck equation, we introduce a geometric framework of non-equilibrium thermodynamics in terms of information geometry and optimal transport theory. We show that the proposed geometric framework is useful for obtaining several non-equilibrium thermodynamic relations, such as thermodynamic trade-off relations between the thermodynamic cost and the fluctuation of the observable, optimal protocols for the minimum thermodynamic cost and the decomposition of the entropy production rate for the non-equilibrium system. We clarify several stochastic-thermodynamic links between information geometry and optimal transport theory via the excess entropy production rate based on a relation between the gradient flow expression and information geometry in the space of probability densities and a relation between the velocity field in optimal transport and information geometry in the space of path probability densities.
