发表机构
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University; Quantum AI & Cyber Security Research Institute, FPT Corporation; Department of Physics, Graduate School of Science, The University of Tokyo; Department of Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心; FPT公司量子AI与网络安全研究所; 东京大学理学研究科物理学系; 京都大学物理学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导欠阻尼朗之万动力学的精确有限时间涨落-响应等式，建立摩擦-响应热力学不确定性关系，揭示响应是关联涨落与耗散的关键量，且该关系可在任意有限观测时间饱和。
AI 中文摘要
热力学不确定性关系将电流涨落与耗散关联起来，通常源于涨落-响应原理。然而在欠阻尼动力学中，传统的平均电流不确定性关系可能失效，而涨落、响应与耗散之间的潜在关联仍不明确。本文通过推导欠阻尼朗之万动力学的精确有限时间涨落-响应等式，揭示了该结构，该等式适用于任意随时间变化的驱动和一般加性可观测量。此等式给出了严格的响应界和动态生成方差的变分表征。选择沿不可逆概率流的扰动，可得到摩擦-响应热力学不确定性关系，该关系能在任意有限观测时间达到饱和，进而为总熵产生建立精确变分原理。我们进一步表明，即使在受驱自由扩散中，速度分辨电流的传统不确定性因子也可随耗散指数衰减，而摩擦-响应因子则保持其通用下界。这些结果确立了响应而非平均电流本身是欠阻尼动力学中直接关联涨落与耗散的量。
英文摘要
Thermodynamic uncertainty relations connect current fluctuations to dissipation and, in certain settings, can emerge from underlying fluctuation-response relations. However, in underdamped dynamics, conventional mean-current uncertainty relations can fail, and the underlying connection between fluctuations, response, and dissipation remains elusive. Here, we uncover this connection by deriving an exact finite-time fluctuation-response equality for underdamped Langevin dynamics, which is valid for arbitrary time-dependent driving and general additive observables. The equality yields sharp response bounds and a variational characterization of the dynamically generated variance. Choosing the perturbation along the irreversible probability flow, we obtain an experimentally accessible friction-response thermodynamic uncertainty relation that is saturable at any finite observation time. It provides both an exact variational principle for entropy production and a weak-noise coherence-dissipation bound for underdamped limit cycles. We further show that the conventional uncertainty factor of velocity-resolved currents can decay exponentially with dissipation, even in driven free diffusion, whereas the friction-response factor retains its universal lower bound. These results establish response, rather than the mean current itself, as the quantity directly linking fluctuations and dissipation in underdamped dynamics.
Comments9+44 pages, 1+1 figures
