发表机构
Institute for Machine Learning (Ellis Unit), Johannes Kepler University; Mistral AI; AMLab, Informatics Institute, University of Amsterdam; CuspAI（约翰开普勒大学（埃利斯单元）机器学习研究所; Mistral AI; 阿姆斯特丹大学信息学研究所AMLab; CuspAI）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究随机系统有限时间驱动的非绝热滞后问题，基于规范型变换构建数值框架，利用刘维尔算子双正交分解产生逆绝热校正，通过数值验证表明该方法能有效抑制非绝热滞后，满足逆绝热条件，使耗散功近似为零。
AI 中文摘要
随机系统的有限时间驱动会产生额外的耗散，使演化的概率分布落后于瞬时平衡，从而降低基于雅津斯基等式的非平衡自由能估计器的收敛性。护送自由能模拟通过设计控制场\(\mathbf{u}\)来解决非绝热滞后问题，该控制场消除滞后，强制轨迹等式\(\mathcal{W}_\mathbf{u} = \Delta \mathcal{F}\)，并产生零方差估计器。然而，以封闭形式构建护送场仍然是一个挑战，目前通过流场方法、目标自由能扰动或学习微分同胚等各种方法来解决。在这项工作中，我们基于规范型变换构建了一个互补的数值框架，而不是基于广义坐标变换，用于基于时间相关的福克 - 普朗克生成器的精确谱分解进行完美护送。刘维尔算子的双正交分解直接产生一个逆绝热校正，其对瞬时平衡分布的作用在形式上类似于量子系统的绝热捷径技术（如贝里的无跃迁驱动），在任意驱动速度下精确抵消非绝热滞后。对时变双阱势和简谐振子中过阻尼粒子模拟的数值验证证实，逆绝热条件在机器精度下得到满足，相对于无护送动力学，非绝热滞后在总变差距离中被抑制了大约十二个数量级，在KL散度中被抑制了十六个数量级。作为一种诊断方法，我们证明了对于所有协议速度下确定性传播的福克 - 普朗克密度，耗散功\(\mathcal{W}_{\text{diss}}(t) \approx 0\)。
英文摘要
Finite-time driving of stochastic systems generates excess dissipation, causing the evolving probability distribution to lag behind the instantaneous equilibrium, and consequently degrading the convergence of nonequilibrium free energy estimators based on the Jarzynski equality. Escorted free energy simulations address the non-adiabatic lag by engineering control fields $\mathbf{u}$ that eliminate the lag, enforcing the trajectory-wise equality $\mathcal{W}_\mathbf{u} = Δ\mathcal{F}$, and yielding zero-variance estimators. However, constructing the escorting field in closed form remains a challenge, approached variously through flow-field methods, targeted free energy perturbation, or learned diffeomorphisms. In this work, we construct a complementary numerical framework based on gauge-type transforms instead of generalized coordinate transforms for perfect escorting based on the exact spectral decomposition of the time-dependent Fokker-Planck generator. The biorthogonal decomposition of the Liouville operator directly yields a counterdiabatic correction whose action on the instantaneous equilibrium distribution exactly cancels the non-adiabatic lag at arbitrary driving speed in formal analogy with shortcuts-to-adiabaticity techniques such as Berry's transitionless driving for quantum systems. Numerical verification for simulations of an overdamped particle in a time-varying double-well potential and harmonic traps confirms that the counterdiabatic condition is satisfied to machine precision, with the non-adiabatic lag suppressed by roughly twelve orders of magnitude in total variation distance and sixteen orders in KL divergence relative to the unescorted dynamics. As a diagnostic, we demonstrate vanishing dissipated work $\mathcal{W}_{\text{diss}}(t) \approx 0$ for the deterministically propagated Fokker-Planck density across all protocol speeds.
Comments34 pages, 13 figures, 14 Tables (including Supplimentary Material)
