arXiv subjects

F. J. Cao

Publications and source records attributed to F. J. Cao.

At least 19 recordsLinked to original sources

arXiv2012

Open Problems on Information and Feedback Controlled Systems

Feedback or closed-loop control allows dynamical systems to increase their performance up to a limit imposed by the second law of thermodynamics. It is expected that within this limit, the system performance increases as the controller uses more information about the system. However, despite the relevant progresses made recently, a general and complete formal development to justify this statement using information theory is still lacking. We present here the state-of-the-art and the main open problems that include aspects of the redundancy of correlated operations of feedback control and the continuous operation of feedback control. Complete answers to these questions are required to firmly establish the thermodynamics of feedback controlled systems. Other relevant open questions concern the implications of the theoretical results for the limitations in the performance of feedback controlled flashing ratchets, and for the operation and performance of nanotechnology devices and biological systems.

cond-mat.stat-mech↗

arXiv2009

Rocking feedback controlled ratchets

We investigate the different regimes that emerge when a periodic driving force, the rocking force, acts on a collective feedback flashing ratchet. The interplay of the rocking and the feedback control gives a rich dynamics with different regimes presenting several unexpected novel features. In particular, we show that for both the one-particle ratchet and the collective version of the ratchet an appropriate rocking increases the flux. This mechanism gives the maximum flux that has been achieved in a ratchet device without an a priori bias.

cond-mat.other↗

arXiv2009

Thermodynamics of feedback controlled systems

We compute the entropy reduction in feedback controlled systems due to the repeated operation of the controller. This was the lacking ingredient to establish the thermodynamics of these systems, and in particular of Maxwell's demons. We illustrate some of the consequences of our general results by deriving the maximum work that can be extracted from isothermal feedback controlled systems. As a case example, we finally study a simple system that performs an isothermal information-fueled particle pumping.

cond-mat.stat-mech↗

arXiv2008

Information and flux in a feedback controlled Brownian ratchet

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.

cond-mat.stat-mech↗

arXiv2008

Optimal operation of feedback flashing ratchets

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off a periodic potential. We discuss different strategies for this operation with the aim of maximizing the net flux of particles in the collective version of a flashing ratchet consisting on N overdamped Brownian particles. We show the optimal protocols for the one-particle ratchet and for the collective ratchet with an infinite number of particles. Finally we comment on the unsolved problem of the optimal strategy for any other number of particles.

cond-mat.stat-mech↗

arXiv2008

Quantum slow-roll and quantum fast-roll inflationary initial conditions: CMB quadrupole suppression and further effects on the low CMB multipoles

Quantum fast-roll initial conditions for the inflaton which are different from the classical fast-roll conditions and from the quantum slow-roll conditions can lead to inflation that last long enough. These quantum fast-roll initial conditions for the inflaton allow for kinetic energies of the same order of the potential energies and nonperturbative inflaton modes with nonzero wavenumbers. Their evolution starts with a transitory epoch where the redshift due to the expansion succeeds to assemble the quantum excited modes of the inflaton in a homogeneous (zero mode) condensate, and the large value of the Hubble parameter succeeds to overdamp the fast-roll of the redshifted inflaton modes. After this transitory stage the effective classical slow-roll epoch is reached. Most of the efolds are produced during the slow-roll epoch and we recover the classical slow-roll results for the scalar and tensor metric perturbations plus corrections. These corrections are important, both for scalar and for tensor perturbations, if scales which are horizon-size today exited the horizon by the end of the transitory stage and as a consequence the lower CMB multipoles get suppressed (fast-roll) or enhanced (precondensate). These two types of corrections can compete and combine in a scale dependent manner. They arise as natural consequences of the quantum nonperturbative inflaton dynamics, and provide a consistent and contrastable model for the origin of the suppression of the quadrupole and for other departures of the low CMB multipoles from the slow-roll inflation-LambdaCMB model which are to be contrasted to the TE and EE multipoles and to the forthcoming and future CMB data.

astro-ph↗

arXiv2008

Transport reversal in a delayed feedback ratchet

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. They can induce directed transport even with symmetric potentials thanks to the asymmetry of the feedback protocol. We investigate here the dynamics of a feedback flashing ratchet when the asymmetry of the ratchet potential and of the feedback protocol favor transport in opposite directions. The introduction of a time delay in the control strategy allows one to nontrivially tune the relative relevance of the competing asymmetries leading to an interesting dynamics. We show that the competition between the asymmetries leads to a current reversal for large delays. For small ensembles of particles current reversal appears as the consequence of the emergence of an open-loop like dynamical regime, while for large ensembles of particles it can be understood as a consequence of the stabilization of quasiperiodic solutions. We also comment on the experimental feasibility of these feedback ratchets and their potential applications.

cond-mat.stat-mech↗

arXiv2008

Flux enhancement and multistability induced by time delays in a feedback controlled flashing ratchet

Feedback controlled ratchets are thermal rectifiers that use information on the state of the system to operate. We study the effects of time delays in the feedback for a protocol that performs an instantaneous maximization of the center-of-mass velocity in the many particle case. For small delays the center-of-mass velocity decreases for increasing delays (although not as fast as in the few particle case). However, for large delays we find the surprising result that the presence of a delay can improve the flux performance of the ratchet. In fact, the maximum flux obtained with the optimal periodic protocol is attained. This implies that the delayed feedback protocol considered can perform better than its non-delayed counterpart. The improvement of the flux observed in the presence of large delays is the result of the emergence of a new dynamical regime where the presence of the delayed feedback stabilizes quasiperiodic solutions that resemble the solutions obtained in a certain closed-loop protocol with thresholds. In addition, in this new regime the system presents multistability, i.e. several quasiperiodic solutions can be stable for a fixed time delay.

cond-mat.stat-mech↗

arXiv2008

How occasional backstepping can speed up a processive motor protein

Fueled by the hydrolysis of ATP, the motor protein kinesin literally walks on two legs along the biopolymer microtubule. The number of accidental backsteps that kinesin takes appears to be much larger than what one would expect given the amount of free energy that ATP hydrolysis makes available. This is puzzling as more than a billion years of natural selection should have optimized the motor protein for its speed and efficiency. But more backstepping allows for the production of more entropy. Such entropy production will make free energy available. With this additional free energy, the catalytic cycle of the kinesin can be speeded up. We show how measured backstep percentages represent an optimum at which maximal net forward speed is achieved.

q-bio.SC↗

arXiv2008

Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz

We present an analytic mean field theory for relaxational dynamics in spatially extended systems that undergo purely noise-induced phase transitions to ordered states. The theory augments the usual mean field approach with a Gaussian ansatz that yields quantitatively accurate results for strong coupling. We obtain analytic results not only for steady state mean fields and distribution widths, but also for the dynamical approach to a steady state or to collective oscillatory behaviors in multi-field systems. Because the theory yields dynamical information, it can also predict the initial-condition-dependent final state (disordered state, steady or oscillatory ordered state) in multistable arrays.

cond-mat.stat-mech↗

arXiv2007

Time-Delayed Feedback control of a flashing ratchet

Closed-loop or feedback control ratchets use information about the state of the system to operate with the aim of maximizing the performance of the system. In this paper we investigate the effects of a time delay in the feedback for a protocol that performs an instantaneous maximization of the center-of-mass velocity. For the one and the few particle cases the flux decreases with increasing delay, as an effect of the decorrelation of the present state of the system with the information that the controller uses, but the delayed closed-loop protocol succeeds to perform better than its open-loop counterpart provided the delays are smaller than the characteristic times of the Brownian ratchet. For the many particle case, we also show that for small delays the center-of-mass velocity decreases for increasing delays. However, for large delays we find the surprising result that the presence of the delay can improve the performance of the nondelayed feedback ratchet and the flux can attain the maximum value obtained with the optimal periodic protocol. This phenomenon is the result of the emergence of a dynamical regime where the presence of the delayed feedback stabilizes one quasiperiodic solution or several (multistability), which resemble the solutions obtained in the so-called threshold protocol. Our analytical and numerical results point towards the feasibility of an experimental implementation of a feedback controlled ratchet that performs equal or better than its optimal open-loop version.

cond-mat.stat-mech↗

arXiv2007

Information and maximum power in a feedback controlled Brownian ratchet

Closed-loop or feedback controlled ratchets are Brownian motors that operate using information about the state of the system. For these ratchets, we compute the power output and we investigate its relation with the information used in the feedback control. We get analytical expressions for one-particle and few-particle flashing ratchets, and we find that the maximum power output has an upper bound proportional to the information. In addition, we show that the increase of the power output that results from changing the optimal open-loop ratchet to a closed-loop ratchet also has an upper bound that is linear in the information.

cond-mat.stat-mech↗

arXiv2007

Out of equilibrium quantum field dynamics in external fields

The quantum dynamics of the symmetry broken λ(Φ^2)^2 scalar field theory in the presence of an homogeneous external field is investigated in the large N limit. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J to -J, gives rise to an out of equilibrium nonperturbative quantum field dynamics. We review here the dynamics for the symmetry broken lambda(Φ^2)^2 scalar N component field theory in the large N limit, with particular stress in the comparison between the results when the initial temperature is zero and when it is finite. The presence of a finite temperature modifies the dynamical effective potential for the expectation value, and also makes that the transition between the two regimes of the early dynamics occurs for lower values of the external field. The two regimes are characterized by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. In the cases when the trapping occurs it is shorter for larger initial temperatures.

hep-ph↗

arXiv2007

Closed-loop control strategy with improved current for a flashing ratchet

We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this article, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.

cond-mat.stat-mech↗

arXiv2006

Quantum inflaton, primordial metric perturbations and CMB fluctuations

We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. Quantum field inflation (under conditions that are the quantum analog of slow roll) leads, upon evolution, to the formation of a condensate starting a regime of effective classical inflation. We compute the primordial perturbations taking the dominant quantum effects into account. The results for the scalar, vector and tensor primordial perturbations are expressed in terms of the classical inflation results. For a N-component field in a O(N) symmetric model, adiabatic fluctuations dominate while isocurvature or entropy fluctuations are negligible. The results agree with the current WMAP observations and predict corrections to the power spectrum in classical inflation. Such corrections are estimated to be of the order of m^2/H^2 where m is the inflaton mass and H the Hubble constant at horizon crossing. This turns to be about 4% for the cosmologically relevant scales. This quantum field treatment of inflation provides the foundations to the classical inflation and permits to compute quantum corrections to it.

astro-ph↗

arXiv2006

Threshold feedback control for a collective flashing ratchet: threshold dependence

We study the threshold control protocol for a collective flashing ratchet. In particular, we analyze the dependence of the current on the values of the thresholds. We have found analytical expressions for the small threshold dependence both for the few and for the many particle case. For few particles the current is a decreasing function of the thresholds, thus, the maximum current is reached for zero thresholds. In contrast, for many particles the optimal thresholds have a nonzero finite value. We have numerically checked the relation that allows to obtain the optimal thresholds for an infinite number of particles from the optimal period of the periodic protocol. These optimal thresholds for an infinite number of particles give good results for many particles. In addition, they also give good results for few particles due to the smooth dependence of the current up to these threshold values.

cond-mat.stat-mech↗

arXiv2006

Domain wall dynamics in expanding spaces

We study the effects on the dynamics of kinks due to expansions and contractions of the space. We show that the propagation velocity of the kink can be adiabatically tuned through slow expansions/contractions, while its width is given as a function of the velocity. We also analyze the case of fast expansions/contractions, where we are no longer on the adiabatic regime. In this case the kink moves more slowly after an expansion-contraction cycle as a consequence of loss of energy through radiation. All these effects are numerically studied in the nonlinear Klein-Gordon equations (both for the sine-Gordon and for the phi^4 potential), and they are also studied within the framework of the collective coordinate evolution equations for the width and the center of mass of the kink. These collective coordinate evolution equations are obtained with a procedure that allows us to consider even the case of large expansions/contractions.

nlin.PS↗

arXiv2006

Out of equilibrium quantum field dynamics of an initial thermal state after a change in the external field

The effects of the initial temperature in the out of equilibrium quantum field dynamics in the presence of an homogeneous external field are investigated. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J to -J, gives rise to an out of equilibrium nonperturbative quantum field dynamics. The dynamics is studied here for the symmetry broken lambda(Phi^2)^2 scalar N component field theory in the large N limit. We find a dynamical effective potential for the expectation value that helps to understand the dynamics. The dynamics presents two regimes defined by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. The two regimes are separated by a critical value of the external field that depends on the initial temperature. The temporal trapping is shorter for larger initial temperatures or larger external fields. Parametric resonances and spinodal instabilities amplify the quantum fluctuations in the field components transverse to the external field. When there is a temporal trapping this is the main mechanism that allows the system to escape from the metastable state for large N. Subsequently backreaction stops the growth of the quantum fluctuations and the system enters a quasiperiodic regime.

hep-ph↗