Maxwell's Demon and the Culture of Entropy

Leff, Harvey S.; Rex, Andrew

doi:10.4006/1.3028691

Cited by 107 publications

(168 citation statements)

References 0 publications

Supporting

Mentioning

156

Contrasting

Unclassified

Order By: Relevance

“…For the computation of this quantity, it is important to note that feedback ratchets have an extra energy input compared to open-loop ratchets, related to the fact that information has an energy cost [13]. This energy cost, known as Landauer's erasure cost because it is incurred when information is erased, effectively prevents Maxwell's demon-type engines, like feedback ratchets, to have efficiencies greater than one (as required by the second law of thermodynamics) [13]. The calculation of this energy cost requires the computation of the mutual information between the controlled system and the controller, conditioned on the past history of the controller's evolution [15,21].…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, we expect Eqs. (13) and (18) to be upper bounds of the maximum flux that can be obtained with a memoryless closed-loop control protocol that uses an amount of information I about the system. Similarly, the inequality shown in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…4, we also discuss the performance of the feedback ratchet as a function of the correlation established between the controlled system and the controller, and briefly discuss other performance measures for feedback ratchets, including the power output and the thermodynamic efficiency. The results that we obtain are in the end specific to the feedback ratchet of [6], but the method that we describe, which is inspired from Maxwell's concept of thermodynamic demons [13], information theory [14] and the work of one of us [15], is general and can be applied to other feedback ratchets and other control systems.…”

Section: Introductionmentioning

confidence: 99%

“…By contrast, the open-loop ratchet induces a flux of particles which is independent of the number of particles. For the remaining, it is useful to picture the ratchet as a Maxwell's demon [13] which rectifies the motion of the Brownian particles by repeatedly estimating the sign of f (t), and by subjecting the particles to the on or off potential depending on the value of the sign measured. When selecting the potential at a given time t, the demon uses only the sign of f (t) or, equivalently, α(t) at time t. It does not use past information about f (t), nor does it use any detailed information about the positions of the particles.…”

Section: Feedback Ratchet and Informationmentioning

confidence: 99%

See 3 more Smart Citations

Information and flux in a feedback controlled Brownian ratchet

Cao

Feito

Touchette

2009

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

We study a feedback control version of the flashing Brownian ratchet, in which the application of the flashing potential depends on the state of the particles to be controlled. Taking the view that the ratchet acts as a Maxwell's demon, we study the relationship that exists between the performance of the demon as a rectifier of random motion and the amount of information gathered by the demon through measurements. In the context of a simple measurement model, we derive analytic expressions for the flux induced by the feedback ratchet when acting on one particle and a few particles, and compare these results with those obtained with its open-loop version, which operates without information. Our main finding is that the flux in the feedback case has an upper bound proportional to the square-root of the information. Our results provide a quantitative analysis of the value of information in feedback ratchets, as well as an effective description of imperfect or noisy feedback ratchets that are relevant for experimental applications.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Feedback Ratchet and Informationmentioning

confidence: 99%

See 2 more Smart Citations

Information and flux in a feedback controlled Brownian ratchet

Cao

Feito

Touchette

2009

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…If the periodic potential is asymmetric, e.g., V ðxÞ ¼ cosð2pxÞ þ ð1=4Þ sinð4pxÞ; and L ¼ 1; the generalized thermodynamic potential CðLÞa0: Consequently, a nonzero stationary drift velocity occurs in the thermal equilibrium state, i.e., an approximation-induced quantum Maxwell demon [15] is seemingly at work.…”

Section: Introductionmentioning

confidence: 99%

The diffusion in the quantum Smoluchowski equation

Łuczka

Rudnicki

Hänggi

2005

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

A novel quantum Smoluchowski dynamics in an external, nonlinear potential has been derived recently. In its original form, this overdamped quantum dynamics is not compatible with the second law of thermodynamics if applied to periodic, but asymmetric ratchet potentials. An improved version of the quantum Smoluchowski equation with a modified diffusion function has been put forward in L. Machura et al. (Phys. Rev. E 70 (2004) 031107) and applied to study quantum Brownian motors in overdamped, arbitrarily shaped ratchet potentials. With this work we prove that the proposed diffusion function, which is assumed to depend (in the limit of strong friction) on the second-order derivative of the potential, is uniquely determined from the validity of the second law of thermodynamics in thermal, undriven equilibrium. Put differently, no approximation-induced quantum Maxwell demon is operating in thermal equilibrium. Furthermore, the leading quantum corrections correctly render the dissipative quantum equilibrium state, which distinctly differs from the corresponding Gibbs state that characterizes the weak (vanishing) coupling limit. r

show abstract

Feedback control in flashing ratchets

et al. 2008

View full text Add to dashboard Cite

In honour of Max Planck (1858Planck ( -1947 on the occasion of his 150th birthday.A flashing ratchet uses a time-dependent, spatially periodic, asymmetric potential to rectify thermal motion of Brownian particles. Here we review approaches to improve the particle flux in this type of Brownian motor by feedback strategies that switch the potential based on the instantaneous particle distribution. We review strategies that are based on the force experienced by the particles, and introduce a new feedback strategy that is based on the expected displacement that can be achieved. Langevin dynamics simulations show that this maximum net displacement strategy performs better than force-based strategies in the limit of very small particle numbers and not too high temperatures. We also review the effects of time delay and noisy channels on feedback control, and perform a feasibility analysis of an experimental system that can realize feedback control using a computer-controlled, scanning-line optical trap and suspended microspheres.

show abstract

Maxwell's Demon and the Culture of Entropy

Cited by 107 publications

References 0 publications

Information and flux in a feedback controlled Brownian ratchet

Information and flux in a feedback controlled Brownian ratchet

The diffusion in the quantum Smoluchowski equation

Feedback control in flashing ratchets

Contact Info

Product

Resources

About