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We explore near-field radiative heat transfer between two bodies under time modulation by developing a rigorous fluctuational electrodynamics formalism. We demonstrate that time modulation can results in the enhancement, suppression, elimination, or reversal of radiative heat flow between the two bodies, and can be used to create a radiative thermal diode with infinite contrast ratio, as well as a near-field radiative heat engine that pumps heat from the cold to the hot bodies. The formalism reveals a fundamental symmetry relation in the radiative heat transfer coefficients that underlies these effects. Our results indicate the significant capabilities of time modulation for managing nanoscale heat flow.

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