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Thermodynamic Uncertainty Relations Including Measurement and Feedback

Patrick P. Potts, Peter Samuelsson

Thermodynamic uncertainty relations quantify how the signal-to-noise ratio of a given observable is constraint by dissipation. Using an intimate connection to fluctuation relations, we extend thermodynamic uncertainty relations to scenarios which include measurement and feedback. Since measurement and feedback generally breaks time-reversal invariance, the uncertainty relations involve quantities averaged over the forward and the backward experiment defined by the associated fluctuation relation. This implies that the signal-to-noise ratio of a given forward experiment can in principle become arbitrarily large as long as the corresponding backward experiment compensates, e.g. by being sufficiently noisy. We illustrate our results with the Szilard engine as well as work extraction by free energy reduction in a quantum dot.

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ArXiv number: 1904.04913