Physical systems powering motion and creating structure in a fixed amount of time dissipate energy and produce entropy. Whether living, synthetic or engineered, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit—a time–information uncertainty relation—imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its s.d. From this general bound, we establish a family of speed limits for heat, dissipated/chemical work and entropy depending on the experimental constraints on the system and its environment. In all of these inequalities, the timescale of transient dynamical fluctuations is universally bounded by the Fisher information. Moreover, they all have a mathematical form that mirrors the Mandelstam–Tamm version of the time–energy uncertainty relation in quantum mechanics. These bounds on the speed of arbitrary observables apply to transient systems away from thermodynamic equilibrium, independent of the physical constraints on the stochastic dynamics or their function.

在固定的时间内为运动提供动力并创建结构的物理系统会耗散能量并产生熵。无论是生活的，合成的还是工程的，执行这些动态功能的系统都必须平衡耗散和速度。在这里，我们表明能量和熵交换的速率受系统信息内容变化速率所强加的速度限制（时间-信息不确定性关系）的影响。这种不确定性关系限制了热力学量的变化与其标准差相同的时间。根据这个一般性的界限，我们根据热量的实验约束建立了热量，耗散/化学功和熵的速度极限族。系统及其环境。在所有这些不平等中，瞬态动力波动的时间尺度通常受Fisher信息的限制。而且，它们都具有反映量子力学中时间-能量不确定性关系的Mandelstam-Tamm版本的数学形式。这些对任意观测速度的限制适用于远离热力学平衡的瞬态系统，而与对随机动力学或其功能的物理约束无关。