Abstract
We calculate analytically the stochastic thermodynamic properties of an isothermal Brownian engine driven by a duo of time-periodic forces, including its Onsager coefficients, the stochastic work of each force, and the corresponding stochastic entropy production. We verify the relations between different operational regimes, maximum power, maximum efficiency, and minimum dissipation, and reproduce the signature features of the stochastic efficiency. All of these results are experimentally tested without adjustable parameters on a colloidal system.
- Received 15 July 2016
DOI:https://doi.org/10.1103/PhysRevX.6.041010
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
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This article appears in the following collection:
Special Collection on Stochastic Thermodynamics
A Physical Review X special collection on stochastic thermodynamics.
Popular Summary
The steam engine was the basis of the industrial revolution, and it also prompted the discovery and development of thermodynamics. The second law of thermodynamics, which limits the efficiency of transforming a heat flux into work, similarly limits the transformation between different forms of work while operating at the same temperature. Such “isothermal engines” are, in fact, ubiquitous in nature. Indeed, on the smallest scales of cellular biology, temperature variations are rare and temperature fluctuations dominate. In such a noisy, fluctuating world, cells must accomplish tasks such as movement or signal detection. Stochastic thermodynamics generalizes thermodynamics to include the effects of such fluctuations and places basic limits on all systems, molecular (e.g., ATP) or otherwise. Here, using this theory, we calculate analytically the stochastic thermodynamic properties of an isothermal Brownian engine consisting of a single Brownian particle confined in a harmonic well and driven by a duo of time-periodic forces.
Our experimental work focuses on a micron-sized colloidal particle (i.e., a silica bead) held in a one-dimensional feedback trap subject to specific electric forces applied every 5 ms. We evaluate the response properties of this Brownian particle to a quadratic potential, and we establish a relation between these quantities and the fluctuating properties. We verify the relations among different operational regimes, maximum power, maximum efficiency, and minimum dissipation and reproduce the signature features of the stochastic efficiency.
We expect that our findings will pave the way for modern-day applications of the tenets of thermodynamics developed nearly 300 years ago.