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.

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• Fluctuation theorems
• Fluctuations & noise
• Noise
• Stochastic processes
• Stochastic thermodynamics
• Markovian processes