Fig. 2 Equivalent electrical network and illustration of the heat flow within the considered thermal connection between a body with heat capacity C at.

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Fig. 2 Equivalent electrical network and illustration of the heat flow within the considered thermal connection between a body with heat capacity C at temperature Tb and another body or a thermal reservoir at Tr. Equivalent electrical network and illustration of the heat flow within the considered thermal connection between a body with heat capacity C at temperature Tb and another body or a thermal reservoir at Tr. (A) The electrical network consists of a Peltier element (Π) with internal resistance R and thermal conductance k in a closed circuit with an ideal inductance L. The oscillatory current I is ultimately driven by the voltages supplied by the thermoelectric effect due to the temperature difference between the cold and the hot end of the Peltier element, and the induced voltage LI. across L (see Eq. 1A). (B) Sketch of the individual contributions to the flow of heat (open arrowheads, arrow lengths not to scale) in Eqs. 1B and 1C for situations when heat is flowing from (filled light/yellow arrows) or to (filled dark/purple arrows) the warmer end of the Peltier element, drawn for one oscillation cycle of Tb(t), as depicted in Fig. 1 (B and D). The thermal oscillator acts during a full period of an oscillation cycle of Tb(t) alternately as a thermoelectric generator (i), a cooler (ii), a generator (iii), and a thermoelectric heater (iv). During all these processes, a small amount of electromagnetic power (LII., green double arrows) is exchanged with the inductor, although the total stored magnetic energy 12LI2 is always less than a fraction Δ0/Tr of the initially deposited excess heat ~ CΔ0 (see text and Fig. 5). A. Schilling et al. Sci Adv 2019;5:eaat9953 Copyright © 2019 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).