Virtual potentials for feedback traps

Jun, Yonggun; Bechhoefer, John

doi:10.1103/physreve.86.061106

Cited by 61 publications

(81 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: Methodsmentioning

confidence: 99%

“…The initial state at time t = 0 is in global equilibrium, with p 0 = 0.5 and H 0 = 1 bit, and ends with H τ , which we control in the range from 0 to 1 bit. The slightly lower energy barrier E b = 10 k B T reduces the distance between wells, which must be large enough that the virtual potential lead to dynamics that are indistinguishable from those of the corresponding physical potential [71]. Because the fixed cycle time is short (≈ 30 s), the probability of a spontaneous hop over the barrier is negligible.…”

mentioning

confidence: 99%

“…By the next cycle, thermal fluctuations have pushed the particle in a different direction, and a new restoring force is computed. Feedback traps can also be used to place particles in a virtual potential, where the motion imitates a desired potential [31,61,71,72].In the protocols described below, we take advantage of the nearly complete freedom to specify arbitrarily the shape of a virtual potential. Thus, we can selectively lower the barrier, while keeping the outer part of the potential fixed.…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Gavrilov

Chétrite

Bechhoefer

2017

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

View full text Add to dashboard Cite

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, for the first time, we measure experimentally this function. 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 twostate 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. INTRODUCTIONBeginning with the foundational work of Clausius, Maxwell, and Boltzmann in the 19th c., the concept of entropy has played a key role in thermodynamics. Yet, despite its importance, entropy is an elusive concept [1][2][3][4][5][6][7][8], with no unique definition; rather, the appropriate definition of entropy depends on the scale, relevant thermodynamic variables, and nature of the system, with ongoing debate existing over the proper definition even for equilibrium cases [9]. Moreover, entropy has not been directly measured but is rather inferred from other quantities, such as the integral of the specific heat divided by temperature. Here, by measuring the work required to erase a fraction of a bit of information, we isolate directly the change in entropy in an open nonequilibrium system, showing that it is compatible with the functional form proposed by Gibbs and Shannon, giving it a physical meaning in this context. Knowing the relevant form of entropy is crucial for efforts to extend thermodynamics to systems out of equilibrium.For a continuous classical system whose state in phase space x is distributed as the probability density function ρ(x), the Gibbs-Shannon entropy is [10,11] where k B is Boltzmann's constant. For quantum systems, von Neumann introduced, in 1927, the corresponding expression in terms of the density matrix [12]. Historically, the system in Eq. 1 has typically been assumed to be in thermal equilibrium. * email: johnb@sfu.caThe physical relevance of Eq. 1 for a nonequilibrium distribution ρ(x) has often been questioned (e.g., [13][14][15][16][17]). One concern is that S is constant on an isolated Hamiltonian system and can change only when evaluated on subsystems, such as those picked out by coarse graining. With many ways to choose subsystems or to coarse grain, is the associated notion of irreversibility intrinsic to the description of the system?In another approach to entropy, advanced in the context of communication and information theory, Shannon [11,18] proved that, up to a multiplicative constant, S is the only possible function satisfying three intuitive axioms. Alternatively, one can start from an...

show abstract

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

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

Gavrilov

Chétrite

Bechhoefer

2017

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, we note that the solid line, calculated according to the theory in Ref. 18, is not a fit but rather a plot, based on parameters taken from the extended-RLS formalism presented here. This agreement justifies the rather complicated extended-RLS analysis of the parameters, the results of which we now describe in detail.…”

Section: Experimental Datamentioning

confidence: 99%

“…Previously, 18 we derived the equations of motion for a particle in a one-dimensional virtual harmonic potential of the form U harm (x) = 1 2 κx 2 , where κ is the force constant and x the displacement from equilibrium. Here, we generalize to the case of motion in an arbitrary, timedependent virtual potential U (x, t) and then derive an alternate form of the equations of motion that is more convenient for numerical simulations and for inferring parameter values.…”

Section: Particle Dynamics In a Feedback Trapmentioning

confidence: 99%

Real-Time Calibration of a Feedback Trap

Gavrilov¹

2017

Experiments on the Thermodynamics of Information Processing

View full text Add to dashboard Cite

Feedback traps use closed-loop control to trap or manipulate small particles and molecules in solution. They have been applied to the measurement of physical and chemical properties of particles and to explore fundamental questions in the non-equilibrium statistical mechanics of small systems. These applications have been hampered by drifts in the electric forces used to manipulate the particles. Although the drifts are small for measurements on the order of seconds, they dominate on time scales of minutes or slower. Here, we show that an extended recursive least-squares (RLS) parameter-estimation algorithm can allow real-time measurement and control of electric and stochastic forces over time scales of hours. Simulations show that the extended-RLS algorithm recovers known parameters accurately. Experimental estimates of diffusion coefficients are also consistent with expected physical properties.

show abstract

Introduction

Kumar

2022

Springer Theses

View full text Add to dashboard Cite

Virtual potentials for feedback traps

Cited by 61 publications

References 26 publications

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

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

Real-Time Calibration of a Feedback Trap

Introduction

Contact Info

Product

Resources

About