Quantum Rayleigh problem and thermocoherent Onsager relations

TL;DR

This paper explores how quantum coherence and correlations influence heat flow and thermoelectric effects, deriving quantum analogs of classical principles and predicting novel thermocoherent phenomena with potential experimental applications.

Contribution

It develops a quantum Rayleigh's heat conduction equation and formulates quantum Onsager relations incorporating quantum discord and entanglement.

Findings

Quantum discord and entanglement contribute to heat flow via heat-exchange coherences.

Quantum Onsager relations predict coherent Peltier and Seebeck effects.

Optimization of effects depends on collision times and collectivity.

Abstract

The role of quantum coherence and correlations in heat flow and equilibration is investigated by exploring the Rayleigh's dynamical problem to equilibration in the quantum regime and following Onsager's approach to thermoelectricity. Specifically, we consider a qubit bombarded by two-qubit projectiles from a side. For arbitrary collision times and initial states, we develop the master equation for sequential and collective collisions. By deriving the Fokker-Planck equation out of the master equation, we identify the quantum version of the Rayleigh's heat conduction equation. We find that quantum discord and entanglement shared between the projectiles can contribute to genuine heat flow only when they are associated with so-called heat-exchange coherences. Analogous to Onsager's use of Rayleigh's principle of least dissipation of energy, we use the entropy production rate to identify the coherence current. Both coherence and heat flows can be written in the form of quantum Onsager relations, from which we predict coherent Peltier and coherent Seebeck effects. The effects can be optimized by the collision times and collectivity. Finally, we discuss some of the possible experimental realizations and technological applications of the thermocoherent phenomena in different platforms.