  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.
