Resumo
We extend the study presented in [Phys. Rev. E 90, 022110 (2014)] to the case of a small
system subject to non-linear interaction and in contact with an athermal shot-noise reservoir.
We rst focus on steady state properties, namely on the impact of the singular measure of the
reservoir in the steady state energy. Then, we introduce the concept of temperatures of higher-
order, which aim to represent the effect produced by the cumulants of the noise of order larger
than 2, and new response functions such as high-order specic heats, that zero out when the
system is thermal or linear. Afterwards, we study the effect of the nature of the noise in the
heat and energy uxes and determine asymptotic expressions for its large deviation functions.
Finally, in analysing the probabilistics of the injected power, jinj, we verify that the exponential
form of its uctuation relation is only asymptotically valid whereas in the thermal case is valid
for all jinj.