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C. A. Plata

Publications and source records attributed to C. A. Plata.

12 recordsLinked to original sources
arXiv2026

Optimal preparation and reachable-state constraints in the Mpemba effect

The Mpemba effect, whereby an initially hotter system relaxes faster than a colder one towards a common final state, is often analysed within the kinetic framework by assuming non-stationary initial conditions that are selected a priori. Here, we revisit this viewpoint by explicitly incorporating the aging protocol used to prepare those states. Focusing on uniformly heated granular fluids, we formulate the preparation stage as an optimal-control problem in which the energy injection is tuned to generate the initial conditions that maximise or minimise the subsequent relaxation rate. Within the first Sonine approximation, this optimisation reduces to extremising the excess kurtosis of the velocity distribution function, the quantity controlling the cooling rate at fixed temperature. Applying Pontryagin's maximum principle, we show that the optimal preparation protocol is always a one-bang protocol and determine the corresponding extremal values of the excess kurtosis. Most importantly, we find that the stochastic thermostat imposes non-trivial reachable-state constraints: the accessible non-Gaussianities are bounded by those of the homogeneous cooling state, thereby limiting the relaxation-rate asymmetry and the maximum attainable Mpemba effect. These results demonstrate that the strength of the kinetic Mpemba effect cannot be disentangled from the accessibility of the underlying non-equilibrium states. More generally, our work establishes a connection between anomalous relaxation, optimal control, and state accessibility in non-equilibrium systems.

cond-mat.stat-mech↗
arXiv2025

Time-optimal synchronisation to self-sustained oscillations under bounded control

Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Liénard system to its limit cycle using a bounded external force. To tackle this challenging non-linear 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.

math.OC↗
arXiv2025

Minimum time connection between non-equilibrium steady states: the Brownian gyrator

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.

cond-mat.stat-mech↗
arXiv2025

Active charge and discharge of a capacitor: scaling solution and energy optimization

Capacitors are ubiquitous in electronic and electrical devices. In this article, we study -- both theoretically and experimentally -- the charging and discharging of capacitors using active control of a voltage source. The energy of these processes is analyzed in terms of work and heat. We show how to approach the quasistatic regime by slowing down the charging or discharging processes. Conversely, we study the price to be paid in terms of Joule heat when we speed up these processes. Finally, we develop optimal processes that minimize energy consumption for a finite charging time. Our work combines fundamental concepts from thermodynamics, classical mechanics and electrical circuits, thus blurring the artificial frontiers at the undergraduate level between these disciplines. Also, it provides a simple example of a prominent problem in current science, the optimization of energy resources. Moreover, our study lends itself well to an experimental project in the classroom, involving computer control of a voltage source, data acquisition, and processing.

physics.ed-ph↗
arXiv2024

Optimal synchronisation to a limit cycle

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 minimising 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 minimising the total work done by the external force.

math-ph↗
arXiv2023

Non-equilibrium memory effects: granular fluids and beyond

In this perspective paper, we look into memory effects in out-of-equilibrium systems. To be concrete, we exemplify memory effects with the paradigmatic case of granular fluids, although extensions to other contexts such as molecular fluids with non-linear drag are also considered. The focus is put on two archetypal memory effects: the Kovacs and Mpemba effects. In brief, the first is related to imperfectly reaching a steady state -- either equilibrium or non-equilibrium, whereas the second is related to reaching a steady state faster despite starting further. Connections to optimal control theory thus naturally emerge and are briefly discussed

cond-mat.stat-mech↗
arXiv2023

Buckling in a rotationally invariant spin-elastic model

Scanning tunneling microscopy experiments have revealed an spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyse an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimisation of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analysed, both analytically and numerically. All phases are characterised by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene.

cond-mat.soft↗
arXiv2020

Finite-time adiabatic processes: derivation and speed limit

Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.

cond-mat.mes-hall↗
arXiv2017

Global stability and $H$-theorem in lattice models with non-conservative interactions

In kinetic theory, a system is usually described by its one-particle distribution function $f(\mathbf{r},\mathbf{v},t)$, such that $f(\mathbf{r},\mathbf{v},t)d\mathbf{r} d\mathbf{v}$ is the fraction of particles with positions and velocities in the intervals $(\mathbf{r}, \mathbf{r}+d\mathbf{r})$ and $(\mathbf{v}, \mathbf{v}+d\mathbf{v})$, respectively. Therein, global stability and the possible existence of an associated Lyapunov function or $H$-theorem are open problems when non-conservative interactions are present, as in granular fluids. Here, we address this issue in the framework of a lattice model for granular-like velocity fields. For a quite general driving mechanism, including both boundary and bulk driving, we show that the steady state reached by the system in the long time limit is globally stable. This is done by proving analytically that a certain $H$-functional is non-increasing in the long time limit. Moreover, for two specific energy injection mechanisms, we are able to demonstrate that the proposed $H$-functional is non-increasing for all times. Also, we put forward a proof that clearly illustrates why the "classical" Boltzmann functional $H_{B}[f]=\int\! d\mathbf{r} \, d\mathbf{v} f(\mathbf{r},\mathbf{v},t) \ln f(\mathbf{r},\mathbf{v},t)$ is inadequate for systems with non-conservative interactions. Not only is this done for the simplified kinetic description that holds in the lattice models analysed here but also for a general kinetic equation, like Boltzmann's or Enskog's.

cond-mat.stat-mech↗
arXiv2016

Lattice models for granular-like velocity fields: Finite-size effects

Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest-neighbour inelastic collisions that conserve momentum but dissipate energy. A set of equations for the fluctuating hydrodynamics of the velocity and energy mesoscopic fields give a first approximation for (i) the velocity structure factor and (ii) the finite-size correction to the Haff law, both in the homogeneous cooling regime. At a more refined level, we have derived the equations for the two-site velocity correlations and the total energy fluctuations. First, we seek a perturbative solution thereof, in powers of the inverse of system size. On the one hand, when scaled with the granular temperature, the velocity correlations tend to a stationary value in the long time limit. On the other hand, the scaled standard deviation of the total energy diverges, that is, the system shows multiscaling. Second, we find an exact solution for the velocity correlations in terms of the spectrum of eigenvalues of a certain matrix. The results of numerical simulations of the microscopic model confirm our theoretical results, including the above described multiscaling phenomenon.

cond-mat.stat-mech↗
arXiv2015

Understanding the dependence on the pulling speed of the unfolding pathway of proteins

The dependence of the unfolding pathway of proteins on the pulling speed is investigated. This is done by introducing a simple one-dimensional chain comprising $N$ units, with different characteristic bistable free energies. These units represent either each of the modules in a modular protein or each of the intermediate "unfoldons" in a protein domain, which can be either folded or unfolded. The system is pulled by applying a force to the last unit of the chain, and the units unravel following a preferred sequence. We show that the unfolding sequence strongly depends on the pulling velocity $v_{p}$. In the simplest situation, there appears a critical pulling speed $v_{c}$: for pulling speeds $v_{p} v_{c}$ it is the pulled unit that unfolds first. By means of a perturbative expansion, we find quite an accurate expression for this critical velocity.

cond-mat.stat-mech↗