The understanding of heat transport in nonequilibrium thermodynamics is an important research frontier, which is crucial for implementing novel thermodynamic devices, such as heat engines and refrigerators. The convection, conduction, and radiation are the well-known basic ways to transfer thermal energy. Here, we demonstrate a different mechanism of phonon heat transport between two spatially separated nanomechanical resonators coupled by the cavity-enhanced long-range interactions. The single trajectory for thermalization and non-equilibrium dynamics is monitored in real-time. In the strong coupling regime, the instant heat flux spontaneously oscillates back and forth in the nonequilibrium steady states. The universal bound on the precision of nonequilibrium steady-state heat flux, i.e. the thermodynamic uncertainty relation, is verified in such a temperature gradient driven far-off equilibrium system. Our results give more insight into the heat transfer with nanomechanical oscillators, and provide a playground for testing fundamental theories in non-equilibrium thermodynamics.

对非平衡热力学中热传递的理解是一个重要的研究前沿，这对于实现新型热力学设备（如热机和冰箱）至关重要。对流、传导和辐射是众所周知的传递热能的基本方式。在这里，我们展示了通过腔增强的长程相互作用耦合的两个空间分离的纳米机械谐振器之间的声子热传输的不同机制。实时监控热化和非平衡动力学的单一轨迹。在强耦合状态下，瞬时热通量在非平衡稳态中自发地来回振荡。非平衡稳态热通量精度的普遍界，即热力学不确定关系，在这种温度梯度驱动的远距离平衡系统中得到了验证。我们的结果更深入地了解纳米机械振荡器的传热，并为测试非平衡热力学的基本理论提供了一个平台。