  Physical systems that power motion and create structure in a fixed amount of
time dissipate energy and produce entropy. Whether living or synthetic, 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 initial standard deviation. From this general bound, we
establish a family of speed limits for heat, work, entropy production, and
entropy flow depending on the experimental constraints on the system. In all of
these inequalities, the time scale 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 assumptions about the stochastic
dynamics or their function.
