Generalized stochastic engines operating in a single spatially homogeneous yet time-dependent bath

In stochastic thermodynamics, molecular machines or motors can operate by harnessing energy from the spatial gradients of either temperature or chemical potential (e.g., nano-Carnot's engines with two thermal baths, or F1-ATPases with two chemical baths of protons). However, it can be energetically costly to create or maintain a sufficient spatial gradient at the length scale of molecules. We argue that enzymes immersed in a temporally changing environment could operate in a brand new regime -- harnessing energy from a single spatially homogeneous bath that varies in time. We provide a minimal solvable model of an enzyme coupled to a bath with time-varying temperature. The periodic variation of the bath then leads to nonzero cyclic currents in the enzyme's state space, which can be used to perform mechanical work or chemical work (i.e., invert the direction of a spontaneous chemical reaction). Analytic solutions to our model can be obtained in the rapid-driving limit. Our model reveals that the wide variety of enzymes existing in living organisms could potentially harness nonequilibrium energy from time-varying environments to perform useful functions.