We study Linear Response Theory and Entropic Fluctuations of finite dimensional non-equilibrium repeated interaction systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different values, we prove analogs of the Green-Kubo fluctuation-dissipation formula and Onsager reciprocity relations on energy flux observables. Then we prove a Large Deviation Principle, or Fluctuation Theorem, and a Central Limit Theorem on the full counting statistics of entropy fluxes. We consider two types of non-equilibrium RIS: either the temperatures of the probes are deterministic and arrive in a cyclic way, or the temperatures of the probes are described by a sequence of i.i.d. random variables with uniform distribution over a finite set.

中文翻译：

---

重复相互作用量子系统中的线性响应理论和熵涨落

我们研究有限维非平衡重复相互作用系统 (RIS) 的线性响应理论和熵涨落。更准确地说，在探针温度可以取有限数量不同值的情况下，我们证明了 Green-Kubo 波动耗散公式和 Onsager 互易关系对能量通量可观测值的模拟。然后我们证明了大偏差原理，或波动定理，以及熵通量全计数统计的中心极限定理。我们考虑两种类型的非平衡 RIS：探针的温度是确定性的并且以循环方式到达，或者探针的温度由在有限集上均匀分布的一系列 iid 随机变量描述。