For small devices, the fluctuations are not negligible so that it is not sufficient to describe them with mean values. We need to use stochastic thermodynamics to take into account those important fluctuations. I will begin to remind some general concepts and results of this theory : stochastic entropy, fluctuation theorem and so on.
On one hand, I will develop a convenient formalism to study efficiency fluctuations of small machines in contact with two reservoirs and I will introduce in particular the large deviation theory. With this tools I will prove that the Carnot efficiency is the least likely in the long time limit, what is actually a consequence of the fluctuation theorem.
On the other hand, I will generalize the formalism to the study of small machines in contact with three reservoirs, the third reservoir modeling unknown losses or eventual helps. I will finish with a application of our theory to a photoelectric device. By assuming a Markovian dynamics we get a master equation that we write with a matrix, the so-called dressed Markov operator. I will show it is possible to deduce very easily a fluctuation relation from this matrix and especially that the greatest eigenvalue is the cumulants generating function (CGF).