Showing papers by "John Bechhoefer published in 2016"

Brownian Duet: A Novel Tale of Thermodynamic Efficiency

Abstract: We thank Laila Singh for suggesting the term "tease." This work was supported by the Flemish Science Foundation (FWO-Vlaanderen) Travel Grant No. K201516N and by a Discovery Grant to J.B. from NSERC (Canada).

Erasure without Work in an Asymmetric Double-Well Potential.

Abstract: Here, we present an experimental study of erasure for a memory encoded in an asymmetric double-well potential. Using a feedback trap, we find that the average work to erase can be less than \(kT\ln 2\).

Arbitrarily slow, non-quasistatic, isothermal transformations

Abstract: Joule or free expansion of an ideal gas into a volume with a lower pressure is an example of an irreversible isothermal process. This nonequilibrium example is often used in traditional thermodynamics text books to demonstrate that an arbitrarily slow process need not be reversible. Cyclic operation of any engine that involves a free expansion is therefore necessary dissipative. Here, we explore experimentally the origin of the thermodynamic irreversibility at the level of a single-particle gas. A feedback trap is used to confine a silica particle in a virtual bistable potential, creating a system analogous to two vessels connected by a valve, where volume of one vessel is adjustable via piston. We operate two types of cyclic transformations, both start and end in the same equilibrium state, and both use the same basic operations—but in different order. One transformation required no work, while the other required work, no matter how slowly it was carried out. A statistical analysis and a recently derived formula are used to show that the difference traces back to the observation that when time is reversed the two protocols have different outcomes. This property is not possible to notice in a single repetition, unlike in a macroscopic system where free expansion is followed by a “whoosh”.

Arbitrarily slow, non-quasistatic, isothermal transformations

Abstract: For an overdamped colloidal particle diffusing in a fluid in a controllable, virtual potential, we show that arbitrarily slow transformations, produced by smooth deformations of a double-well potential, need not be reversible. The arbitrarily slow transformations do need to be fast compared to the barrier crossing time, but that time can be extremely long. We consider two types of cyclic, isothermal transformations of a double-well potential. Both start and end in the same equilibrium state, and both use the same basic operations---but in different order. By measuring the work for finite cycle times and extrapolating to infinite times, we found that one transformation required no work, while the other required a finite amount of work, no matter how slowly it was carried out. The difference traces back to the observation that when time is reversed, the two protocols have different outcomes, when carried out arbitrarily slowly. A recently derived formula relating work production to the relative entropy of forward and backward path probabilities predicts the observed work average.

Feedback traps for virtual potentials

Abstract: Feedback traps are tools for trapping and manipulating single charged objects, such as molecules in solution. An alternative to optical tweezers and other single-molecule techniques, they use feedback to counteract the Brownian motion of a molecule of interest. The trap first acquires information about a molecule's position and then applies an electric feedback force to move the molecule. Since electric forces are stronger than optical forces at small scales, feedback traps are the best way to trap single molecules without "touching" them. Feedback traps can do more than trap molecules: They can also subject a target object to forces that are calculated to be the gradient of a desired potential function U(x). If the feedback loop is fast enough, it creates a virtual potential whose dynamics will be very close to those of a particle in an actual potential U(x). But because the dynamics are entirely a result of the feedback loop--absent the feedback, there is only an object diffusing in a fluid--we are free to specify and then manipulate in time an arbitrary potential U(x,t). Here, we review recent applications of feedback traps to studies on the fundamental connections between information and thermodynamics, a topic where feedback plays an even more-fundamental role. We discuss how recursive maximum likelihood techniques allow continuous calibration, to compensate for drifts in experiments that last for days. We consider ways to estimate work and heat to a precision of 0.03 kT over these long experiments. Finally, we compare work and heat measurements of the costs of information erasure, the Landauer limit of kT ln2 per bit of information erased. We argue that when you want to know the average heat transferred to a bath in a long protocol, you should measure instead the average work and then infer the heat using the first law of thermodynamics.

Brownian duet: A novel tale of thermodynamic efficiency

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 these results are experimentally tested without adjustable parameters on a colloidal system.