We explore whether localized surface plasmon polariton modes can transfer heat between molecules placed in the hot spot of a nanoplasmonic cavity through optomechanical interaction with the molecular vibrations. We demonstrate that external driving of the plasmon resonance indeed induces an effective molecule-molecule interaction corresponding to a new heat transfer mechanism, which can even be more effective in cooling the hotter molecule than its heating due to the vibrational pumping by the plasmon. This novel mechanism allows to actively control the rate of heat flow between molecules through the intensity and frequency of the driving laser.

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We theoretically study a hybrid plasmonic-photonic cavity setup that can be used to induce and control long-distance heat transfer between molecular systems through optomechanical interactions. The structure we propose consists of two separated plasmonic nanoantennas coupled to a dielectric cavity. The hybrid modes of this resonator can combine the large optomechanical coupling of the sub-wavelength plasmonic modes with the large quality factor and delocalized character of the cavity mode that extends over a large distance (∼µm). We show that this can lead to effective long-range heat transport between molecular vibrations that can be actively controlled through an external driving laser.

By introducing thermo-entangled state representation , which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using ''dissipative interaction picture we solve the master equation of Jaynes-Cummings model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state and the cavity mode is in coherent state.

By virtue of the thermo-entangled states representation of density operator and using "dissipative interaction picture" we solve the master equation of a driven damped harmonic oscillator in a squeezed bath. We show that the essential part of the dynamics can be expressed by the convolution of initial Wigner function with a special kind of normalized Gaussian in phase space and relate the dynamics with the change of Gaussian ordering of density operator.