The second law of thermodynamics dictates that heat simultaneously flows from the hot to cold bath on average. To go beyond this picture, a range of works in the past decade show that, other than the average dynamical heat flux determined by instantaneous thermal bias, a non-trivial flux contribution of intrinsic geometric origin is generally present in temporally driven systems. This additional heat flux provides a free lunch for the pumped heat and could even drive heat against the bias. We review here the emergence and development of this so called “geometric heat pump”, originating from the topological geometric phase effect, and cover various quantum and classical transport systems with different internal dynamics. The generalization from the adiabatic to the non-adiabatic regime and the application of control theory are also discussed. Then, we briefly discuss the symmetry restriction on the heat pump effect, such as duality, supersymmetry and time-reversal symmetry. Finally, we examine open problems concerning the geometric heat pump process and elucidate their prospective significance in devising thermal machines with high performance.

热力学第二定律规定热量平均同时从热浴流向冷浴。为了超越这幅图，过去十年的一系列工作表明，除了由瞬时热偏差确定的平均动态热通量外，时间驱动系统中通常存在固有几何起源的非平凡通量贡献。这种额外的热通量为泵送的热量提供了免费午餐，甚至可以驱动热量对抗偏差。我们在这里回顾了这种所谓的“几何热泵”的出现和发展，它起源于拓扑几何相效应，涵盖了具有不同内部动力学的各种量子和经典传输系统。还讨论了从绝热状态到非绝热状态的推广以及控制理论的应用。然后，我们简要讨论了热泵效应的对称性限制，例如对偶性、超对称性和时间反转对称性。最后，我们研究了有关几何热泵过程的开放性问题，并阐明了它们在设计高性能热机方面的前瞻性意义。