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We propose a new mechanism that enables heat flow from a colder region to ahotter region without necessitating either particle transport or external workon the conductor, thereby bypassing the compressor part of a classical heatpump cycle. Our mechanism relies on thermostatting the kinetic andconfigurational temperatures of the same particle differently. We keep the twoends of a conductor, which in the present study is a single dimensional$\phi^4$ chain, at the same kinetic temperature $T_0$, but at differentconfigurational temperatures - one end hotter and the other end colder than$T_0$. While external energy is needed within the thermostatted regions toachieve this differential thermostatting, no external work is performed on thesystem itself. We show that the mechanism satisfies the statistical form of thesecond law of thermodynamics (the fluctuation theorem). The proposed mechanismreveals two interesting findings - (i) contrary to traditional thermodynamicswhere only the kinetic temperature is thought to govern heat conduction,configurational temperature can also play an important role, and (ii) therelative temperature difference between the kinetic and configurationalvariables governs the direction of heat flow. The challenge, however, is indeveloping experimental techniques to thermostat the kinetic andconfigurational variables of the same particle at different values.

Heat pump without particle transport or external work on the medium achieved by differential thermostatting of the phase space