Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.

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循环驱动输运中非平衡涨落的热力学几何

循环驱动下的非平衡热机通常优于稳态热机。然而，对于时间调制下的多功能输运和涨落特征仍然缺乏连贯的理解。在这里，我们根据非平衡驱动输运的全面计数统计制定了热力学几何的理论框架。我们发现，除了传统的动态和绝热几何曲率贡献之外，生成函数还分为额外的非绝热贡献，表现为全计数统计的度量项。这种非绝热度量将近平衡熵产生中热力学几何的最新结果推广到一般电流的远非平衡波动。此外，该框架证明了近绝热热装置的几何热力学不确定性关系，限制了统计度量量和热力学长度方面的波动。我们在实验上可实现的驱动诱导量子手性输运和布朗热泵中举例说明了该理论。