  The time-periodic modulation of a temperature gradient can alter the heat
transport properties of a physical system. Oscillating thermal gradients give
rise to behaviors such as modified thermal conductivity and controllable
time-delayed energy storage that are not present in a system with static
temperatures. Here, we examine how the heat transport properties of a molecular
lattice model are affected by an oscillating temperature gradient. We use
analytical analysis and molecular dynamics simulations to investigate the
vibrational heat flow in a molecular lattice system consisting of a chain of
particles connected to two heat baths at different temperatures, where the
temperature difference between baths is oscillating in time. We derive
expressions for heat currents in this system using a stochastic energetics
framework and a nonequilibrium Green's function approach that is modified to
treat the nonstationary average energy fluxes. We find that emergent energy
storage, energy release, and thermal conductance mechanisms induced by the
temperature oscillations can be controlled by varying the frequency, waveform,
and amplitude of the oscillating gradient. The developed theoretical approach
provides a general framework to describe how vibrational heat transmission
through a molecular lattice is affected by temperature gradient oscillations.
