Zhong Adrianne, DeWeese Michael R
Department of Physics, <a href="https://ror.org/01an7q238">University of California, Berkeley</a>, Berkeley, California 94720, USA.
Redwood Center for Theoretical Neuroscience, <a href="https://ror.org/01an7q238">University of California, Berkeley</a>, Berkeley, California 94720, USA.
Phys Rev Lett. 2024 Aug 2;133(5):057102. doi: 10.1103/PhysRevLett.133.057102.
A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a Riemannian metric defined on control space. For overdamped dynamics in arbitrary dimensions, we demonstrate that thermodynamic geometry is equivalent to L^{2} optimal transport geometry defined on the space of equilibrium distributions corresponding to the control parameters. We show that obtaining optimal protocols past the slow-driving or linear response regime is computationally tractable as the sum of a friction tensor geodesic and a counterdiabatic term related to the Fisher information metric. These geodesic-counterdiabatic optimal protocols are exact for parametric harmonic potentials, reproduce the surprising nonmonotonic behavior recently discovered in linearly biased double well optimal protocols, and explain the ubiquitous discontinuous jumps observed at the beginning and end times.
热力学几何的一个基本结果是，在慢驱动极限下驱动非平衡系统在两个热力学状态之间的最优、最小功协议由摩擦张量的测地线给出，摩擦张量是定义在控制空间上的黎曼度量。对于任意维度的过阻尼动力学，我们证明热力学几何等同于定义在与控制参数对应的平衡分布空间上的(L^{2})最优传输几何。我们表明，在慢驱动或线性响应 regime 之外获得最优协议在计算上是易于处理的，因为它是摩擦张量测地线和与费希尔信息度量相关的反绝热项的总和。这些测地线 - 反绝热最优协议对于参数谐波势是精确的，再现了最近在线性偏置双阱最优协议中发现的令人惊讶的非单调行为，并解释了在开始和结束时间观察到的普遍存在的不连续跳跃。
