Antonio Prados

We consider overdamped physical systems evolving under a feedback-controlled fluctuating potential and in contact with a thermal bath at temperature T. A Markovian description of the dynamics, which keeps only the last value of the control action, is advantageous-both from the theoretical and the practical side-for the entropy balance. Novel second-law equalities and bounds for the extractable work are obtained, the latter being both tighter and easier to evaluate than those in the literature based on the whole chain of controller actions. The Markovian framework also allows us to prove that the bound for the extractable work that incorporates the unavailable information is saturated in a wide class of physical systems, for error-free measurements. These results are illustrated in model systems. For imperfect measurements, there appears an interval of measurement uncertainty, including the point at which work ceases to be extracted, where the new Markovian bound is tighter than the unavailable information bound.

We investigate the search of a target with a given spatial distribution in a finite one-dimensional domain. The searcher follows Brownian dynamics and is always reset to its initial position when reaching the boundaries of the domain (boundary resetting). In addition, the searcher may be reset to its initial position from any internal point of the domain (bulk resetting). Specifically, we look for the optimal strategy for bulk resetting, i.e., the spatially dependent bulk resetting rate that minimizes the average search time. The best search strategy exhibits a second-order transition from vanishing to nonvanishing bulk resetting when varying the target distribution. The obtained mathematical criteria are further analyzed for different monoparametric families of distributions, which sheds light on the properties that control the optimal strategy for bulk resetting. Our work defines a distinct research direction in the study of search processes, emphasizing the relevance of the target distribution for optimal search strategies, and identifies a successful framework to address these questions.

Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronization of a Liénard system to its limit cycle using a bounded external force. To tackle this challenging nonlinear optimal control problem, our approach involves applying Pontryagin’s maximum principle with a combination of analytical and numerical tools. We show that the optimal control develops a remarkably complex structure in phase space as the force bound is lowered. Trajectories rewound from the limit cycle’s extreme points turn out to play a key role in determining the maximum number of control bangs for optimal connection. We illustrate these intricate features using the paradigmatic van der Pol oscillator model.

Optimal control of levitated nanoparticles subjected to thermal fluctuations is a challenging problem, both theoretically and experimentally. In this Letter, we compute the time-dependent harmonic confining potential that steers, in a prescribed time and with the minimum energetic cost, a Brownian particle between two assigned equilibrium states. We take full account of inertial effects, thus addressing the general underdamped dynamics, and, to address actual experimental conditions, the stiffness of the confining potential is required to be bounded. We carry out an experiment realizing the described protocol for an optically confined nanoparticle, which is shown to reach the target state within accuracy-while spending less energy than other protocols with the same duration, significantly shorter than the characteristic relaxation time. The results presented here are expected to have relevant applications in the design of optimal devices, such as engines at the nanoscale.

Plasma treatment of seeds is an efficient procedure to accelerate germination, to improve initial stages of plant growth, and for protection against pathogen infection. Most studies relate these beneficial effects with biochemical modifications affecting the metabolism and genetic growth factors of seeds and young plants. Using barley seeds, in this work, we investigate the redistribution of ions in the seed surface upon their treatment with cold air plasmas. In addition, we investigate the effect of plasma in the lixiviation of ions through the seeds' hull when they are immersed in water. Ion redistribution in the outer layers of air plasma-treated seeds has been experimentally determined through X-ray photoelectron spectroscopy analysis in combination with in-depth chemical profiling with gas cluster ion beams. The results show that in the shallowest layers of the seed hull (at least up to a depth of ∼100 nm) there is an enrichment of K⁺ and Ca²⁺ ions, in addition to changes in the O/C and N/C atomic ratios. These data have been confirmed by the electron microscopy/fluorescence analysis of seed cuts. Observations have been accounted for by a Monte Carlo model, simulating the electrostatic interactions that develop between the negative charge accumulated at the seed surface due to the interaction with the plasma sheath and the positive ions existing in the interior. Furthermore, it is shown that upon water immersion of plasma-treated seeds mobilized ions tend to lixiviate more efficiently than in pristine seeds. The detection of a significant concentration of NO₃^- anions in the water has been attributed to a secondary reaction of nitrogen species incorporated into the seeds during plasma exposure with reactive oxygen species formed on their surface during this treatment. The implications of these findings for the improvement of the germination capacity of seeds are discussed.

Heat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in recent decades allow for expanding the experimental possibilities and designing engines operating with a single particle. In this case, the system of interest cannot be addressed at a macroscopic level and their study is framed in the field of stochastic thermodynamics. In the present work, we study mesoscopic heat engines built with a Brownian particle submitted to harmonic confinement and immersed in a fluid acting as a thermal bath. We design a Stirling-like heat engine, composed of two isothermal and two isochoric branches, by controlling both the stiffness of the harmonic trap and the temperature of the bath. Specifically, we focus on the irreversible, non-quasi-static case—whose finite duration enables the engine to deliver a non-zero output power. This is a crucial aspect, which enables the optimisation of the thermodynamic cycle by maximising the delivered power—thereby addressing a key goal at the practical level. The optimal driving protocols are obtained by using both variational calculus and optimal control theory tools. Furthermore, we numerically explore the dependence of the maximum output power and the corresponding efficiency on the system parameters.

We study the relaxation of the Metropolis Monte Carlo algorithm corresponding to a single particle trapped in a one-dimensional confining potential, with even jump distributions that ensure that the dynamics verifies detailed balance: in particular, how can one minimise the characteristic time for reaching the target equilibrium probability distribution function? To work out the corresponding optimal sampling method, we study the physical mechanisms that affect the dynamics. Previous work suggested that, for smooth jump distributions, the fastest convergence rate is obtained as a result of the competition between diffusive and rejection-dominated dynamics. In this work, we show that a new relevant physical regime comes into play for two-peaked jump distributions, where the relaxation dynamics is dominated neither by diffusion nor by rejection: the eigenmodes adopt an oscillatory form, reminiscent of charge density waves (CDW)—thus we term this new regime the CDW regime. Using a combination of numerical and analytical techniques, the parameter regions corresponding to diffusion, rejection, and CDW are characterised, as well as the transition lines between them. Therefore, a phase diagram is built, in which there are two order parameters characterising each of the phase transitions: the Inverse Participation Ratio and the Fidelity—reminiscent of the quantum fidelity. The optimal convergence rate is located at the triple point of phase coexistence, where the transition lines (diffusive-rejection, diffusive-CDW, and CDW-rejection) intersect. We then address the fundamental problem of finding the optimal jump distribution, without any assumption on its functional form. Our theoretical framework is checked against the numerical diagonalisation of the master equation for the case of harmonic confinement, which is the paradigmatic example of a convex potential with only one minimum. We also briefly discuss more sophisticated attempts at optimising the convergence rate to equilibrium.

We study the problem of minimising the connection time between non-equilibrium steady states of the Brownian gyrator. This is a paradigmatic model in non-equilibrium statistical mechanics, an overdamped Brownian particle trapped in a two-dimensional elliptical potential, with the two degrees of freedom (x, y) coupled to two, in principle different, thermal baths with temperatures T_x and T_y , respectively. Application of Pontryagin’s Maximum Principle reveals that shortest protocols belong to the boundaries of the control set defined by the limiting values of the parameters (k, u) characterising the elliptical potential. We identify two classes of optimal minimum time protocols, i.e. brachistochrones: (i) regular bang–bang protocols, for which (k, u) alternatively take their minimum and maximum values allowed, and (ii) infinitely degenerate singular protocols. We thoroughly investigate the minimum connection time over the brachistochrones in the limit of having infinite capacity for compression. A plethora of striking phenomena emerge: sets of states attained at null connection times, discontinuities in the connection time along adjacent target states, and the fact that, starting from a state in which the oscillators are coupled, uncoupled states are impossible to reach in a finite time.

In the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic trajectory—the limit cycle—after infinite time. Here, we drive the van der Pol oscillator with an external time-dependent force to reach the limit cycle in a given finite time. Specifically, we are interested in minimizing the non-conservative contribution to the work when driving the system from a given initial point on the phase plane to any final point belonging to the limit cycle. There appears a speed-limit inequality, which expresses a trade-off between the connection time and cost—in terms of the non-conservative work. We show how the above results can be generalized to the broader family of non-linear oscillators given by the Liénard equation. Finally, we also look into the problem of minimizing the total work done by the external force.

In feedback-controlled systems, an external agent—the feedback controller—measures the state of the system and modifies its subsequent dynamics depending on the outcome of the measurement. In this paper, we build a Markovian description for the joint stochastic process that comprises both the system and the controller variables. This Markovian description is valid for a wide class of feedback-controlled systems, allowing for the inclusion of errors in the measurement. The general framework is motivated and illustrated with the paradigmatic example of the feedback flashing ratchet.