Entropy production of nano systems with timescale separation

Abstract

Energy flow in bio-molecular motors and machines are vital to their function. Yet experimental observations are often limited to a small subset of variables that participate in energy transport and dissipation. Here we show, through a solvable Langevin model, that the seemingly hidden entropy production is measurable through the violation spectrum of the fluctuation-response relation of a slow observable. For general Markov systems with timescale separation, we prove that the violation spectrum exhibits a characteristic plateau in the intermediate frequency region. Despite its vanishing height, the plateau can account for energy dissipation over a broad timescale. Our findings suggest a general possibility to probe hidden entropy production in nano systems without direct observation of fast variables.

14 pages, 6 figures

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• Fluctuation relations and coarse-graining
• Entropy production and coarse-graining in Markov processes
• Experimental Test of a New Equality: Measuring Heat Dissipation in an Optically Driven Colloidal System
• Nonequilibrium fluctuation-dissipation theorem and heat production
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