Moments of Entropy Production in Dissipative Devices

We characterize the possible moments of entropy production for overdamped stationary Markov processes. We find a general formulation of the problem, and derive a new necessary condition relating the second and third moments. We determine all possible first, second, and third moments of entropy production for a white noise process. As a consequence, we obtain a lower bound for the skewness of the current fluctuations in dissipative devices such as transistors, thereby demonstrating that the Gaussianity assumption widely used, e.g., in electronic engineering is thermodynamically inconsistent.