Showing papers by "John Bechhoefer published in 2017"

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Abstract: Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here we measure experimentally this function in a system that is in local but not global equilibrium. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a two-state system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds.

Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics.

Abstract: The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-square displacement grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar substrate. Because the local effective diffusivity is known, we have been able to carry out a direct test of this mechanism for diffusion in inhomogeneous media.

When memory pays: Discord in hidden Markov models

Abstract: When is keeping a memory of observations worthwhile? We use hidden Markov models to look at phase transitions that emerge when comparing state estimates in systems with discrete states and noisy observations. We infer the underlying state of the hidden Markov models from the observations in two ways: through naive observations, which take into account only the current observation, and through Bayesian filtering, which takes the history of observations into account. Defining a discord order parameter to distinguish between the different state estimates, we explore hidden Markov models with various numbers of states and symbols and varying transition-matrix symmetry. All behave similarly. We calculate analytically the critical point where keeping a memory of observations starts to pay off. A mapping between hidden Markov models and Ising models gives added insight into the associated phase transitions.

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 molecule9s 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 (e.g. by putting them in a small box or attaching them to a tether). 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, using them to measure fluctuating energies 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 ln 2 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. This article is part of the themed issue ‘Horizons of cybernetical physics’.

Feedback traps and the generalized Landauer limit for erasing information

Abstract: We review studies based on feedback traps of the fundamental thermodynamic limits for information erasure (generalized Landauer limit). We report the first direct measurement of nonequilibrium system entropy, showing it matches Shannon’s expression. OCIS codes: 350.4855, 110.0180, 000.6850, 140.7010. 1. Feedback traps and their applications to the stochastic thermodynamics of small systems In 2005, Cohen and Moerner developed the Anti-Brownian Electrokinetic (ABEL) trap, a new tool for trapping and manipulating small objects in solution [1]. The idea, to trap small objects by counteracting Brownian motion using a feedback loop, is illustrated in Fig. 1. One measures the position of an object in the trap, for example, by taking a camera image and using image processing to find the object’s coordinates. Then one computes and applies the desired force F to the charged particles via a voltage V . To emphasize the generality of the technique, we adopt the more generic name of feedback trap. In the trap used for the bulk of the experiments reported here, the loop cycle time was 5 ms, and the bead was 1.5 μm in diameter. The silica bead had a density large enough to confine the particle near the bottom of the sample cell while still allowing horizontal diffusion.

Direct measurement of a nonequilibrium system entropy using a feedback trap

Abstract: Feedback traps are tools for trapping single charged objects in solution. They periodically measure an object’s position and apply a feedback force to counteract Brownian motion. The feedback force can be calculated as a gradient of a potential function, effectively creating a “virtual potential.” Its flexibility regarding the choice of form of the potential gives an opportunity to explore various fundamental questions in stochastic thermodynamics. Here, we review the theory behind feedback traps and apply it to measuring the average work required to erase a fraction of a bit of information. The results agree with predictions based on the nonequilibrium system entropy. With this example, we also show how a feedback trap can easily implement the complex erasure protocols required to reach ultimate thermodynamic limits.

From rods to blobs: When geometry is irrelevant for heat diffusion

Abstract: Thermal systems are an attractive setting for exploring the connections between the lumped-element approximations of elementary circuit theory and the partial-differential field equations of mathematical physics, a topic that has been neglected in physics curricula. In a calculation suitable for an undergraduate course in mathematical physics, we show that the response function between an oscillating heater and temperature probe has a smooth crossover between a low-frequency, "lumped-element" regime where the system behaves as an electrical capacitor and a high-frequency regime dominated by the spatial dependence of the temperature field. Undergraduates can easily (and cheaply) explore these ideas experimentally in a typical advanced laboratory course. Because the characteristic frequencies are low, ($\approx$ 30 s)$^{-1}$, measuring the response frequency by frequency is slow and challenging; to speed up the measurements, we introduce a useful, if underappreciated experimental technique based on a multisine power signal that sums carefully chosen harmonic components with random phases. Strikingly, we find that the simple model of a one-dimensional, finite rod predicts a temperature response in the frequency domain that closely approximates experimental measurements from an irregular, blob-shaped object. The unexpected conclusion is that the frequency response of this irregular thermal system is nearly independent of its geometry, an example of---and justification for---the "spherical cow" approximations so beloved of physicists.