Searcharxiv⌕ Search

arXiv subjects

Édgar Roldán

Publications and source records attributed to Édgar Roldán.

At least 37 records · Page 2Linked to original sources
arXiv2024

Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times

Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times, unidirectional (possibly deterministic) transitions, and restricted initial conditions, features common in real-world computers. Here, we present a framework which tackles all such difficulties by extending the martingale theory of non-equilibrium thermodynamics to generic non-stationary Markovian processes, including those with broken detailed balance and/or absolute irreversibility. We derive several universal fluctuation relations and second-law-like inequalities that provide both lower and upper bounds on the intrinsic dissipation (mismatch cost) associated with any periodic process -- in particular the periodic processes underlying all current digital computation. Crucially, these bounds apply even if the process has stochastic stopping times, as it does in many computational machines. We illustrate our results with exhaustive numerical simulations of deterministic finite automata (DFA) processing bit strings, one of the fundamental models of computation from theoretical computer science. We also provide universal equalities and inequalities for the acceptance probability of words of a given length by a deterministic finite automaton in terms of thermodynamic quantities, and outline connections between computer science and stochastic resetting. Our results, while motivated from the computational context, are applicable far more broadly.

cond-mat.stat-mech↗
arXiv2023

The impact of memory on learning sequence-to-sequence tasks

The recent success of neural networks in natural language processing has drawn renewed attention to learning sequence-to-sequence (seq2seq) tasks. While there exists a rich literature that studies classification and regression tasks using solvable models of neural networks, seq2seq tasks have not yet been studied from this perspective. Here, we propose a simple model for a seq2seq task that has the advantage of providing explicit control over the degree of memory, or non-Markovianity, in the sequences -- the stochastic switching-Ornstein-Uhlenbeck (SSOU) model. We introduce a measure of non-Markovianity to quantify the amount of memory in the sequences. For a minimal auto-regressive (AR) learning model trained on this task, we identify two learning regimes corresponding to distinct phases in the stationary state of the SSOU process. These phases emerge from the interplay between two different time scales that govern the sequence statistics. Moreover, we observe that while increasing the integration window of the AR model always improves performance, albeit with diminishing returns, increasing the non-Markovianity of the input sequences can improve or degrade its performance. Finally, we perform experiments with recurrent and convolutional neural networks that show that our observations carry over to more complicated neural network architectures.

cs.LG↗
arXiv2023

Taxis of cargo-carrying microswimmers in traveling activity waves

Many fascinating properties of biological active matter crucially depend on the capacity of constituting entities to perform directed motion, e.g., molecular motors transporting vesicles inside cells or bacteria searching for food. While much effort has been devoted to mimicking biological functions in synthetic systems, such as transporting a cargo to a targeted zone, theoretical studies have primarily focused on single active particles subject to various spatial and temporal stimuli. Here we study the behavior of a self-propelled particle carrying a passive cargo in a travelling activity wave and show that this active-passive dimer displays a rich, emergent tactic behavior. For cargoes with low mobility, the dimer always drifts in the direction of the wave propagation. For highly-mobile cargoes, instead, the dimer can also drift against the traveling wave. The transition between these two tactic behaviors is controlled by the ratio between the frictions of the cargo and the microswimmer. In slow activity waves the dimer can perform an active surfing of the wave maxima, with an average drift velocity equal to the wave speed. These analytical predictions, which we confirm by numerical simulations, might be useful for the future efficient design of bio-hybrid microswimmers.

cond-mat.stat-mech↗
arXiv2022

What to learn from a few visible transitions' statistics?

Interpreting partial information collected from systems subject to noise is a key problem across scientific disciplines. Theoretical frameworks often focus on the dynamics of variables that result from coarse-graining the internal states of a physical system. However, most experimental apparatuses can only detect a partial set of transitions, while internal states are inaccessible. Here, we consider an observer who records a time series of occurrences of one or several transitions performed by a system, under the assumption that its underlying dynamics is Markovian. We pose the question of how one can use the transitions' information to make inferences of dynamical, thermodynamical, and biochemical properties. First, elaborating on first-passage time techniques, we derive analytical expressions for the probabilities of consecutive transitions and the time elapsed between them. Second, we derive a lower bound for the entropy production rate that equals the sum of two non-negative contributions, one due to the statistics of transitions and a second due to the statistics of inter-transition times. We also show that when only one current is measured, our estimate still detects irreversibility even in the absence of net currents. We illustrate the developed framework in experimentally-validated biophysical models of kinesin and dynein molecular motors, and in a minimal model for template-directed polymerization. Our results reveal that while entropy production is entailed in the statistics of two successive transitions of the same type, the statistics of two different successive transitions can probe the existence of an underlying disorder in the motion of a molecular motor. Taken all together, our results highlight the power of inference from transition statistics ranging from thermodynamic quantities to network-topology properties of Markov processes.

cond-mat.stat-mech↗
arXiv2022

Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics

Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g. the diffusion coefficient or the heat conductivity which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated, because two alternative formulations of the inhomogeneous transport equations exist in the literature -- the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Buettikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film.

cond-mat.stat-mech↗
arXiv2022

Modelling Active Non-Markovian Oscillations

Modelling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a non-Markovian bistable noise that is capable of generating self-sustained periodic oscillation. We derive analytical predictions for most relevant dynamical and thermodynamic properties of the model. This minimal model turns out to describe accurately bistable-like oscillatory motion of hair bundles in bullfrog sacculus, extracted from experimental data. Based on and in agreement with these data, we estimate the power required to sustain such active oscillations to be of the order of one hundred $k_B T$ per oscillation cycle.

cond-mat.stat-mech↗
arXiv2022

Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines

We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent thresholds that these quantities does not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results entail an extension of martingale theory for entropy production, for which we derive universal inequalities involving its maximum and minimum statistics that are valid for generic Markovian dynamics in non-equilibrium stationary states. We test our main results with numerical simulations of a stochastic photoelectric device.

cond-mat.stat-mech↗
arXiv2021

Learning the Hydrophilic, Hydrophobic and Aromatic Character of Amino Acids from their Interfacial Thermal Conductance in Water

In this study, the thermal relaxation of the 20 naturally occurring amino-acids in water is investigated using transient non-equilibrium molecular-dynamics simulations. By modeling the thermal relaxation process, the relaxation times of the amino-acids in water occurs over a timescale covering 2-5 ps. For the hydrophobic amino acids, the relaxation time is controlled by the size of the hydrocarbon side chain, while for hydrophilic amino acids, the number of hydrogen bonds do not significantly affect the timescales of the heat dissipation. Our results show that the interfacial thermal conductance at the amino-acid water interface is in the range of~40-80 MWm$^{-2}$K$^{-1}$. Hydrophobic and aromatic amino acids tend to have a lower interfacial thermal conductance. Notably, we reveal that amino acids can be classified, in terms of their thermal relaxation times and molar masses, into simply connected phases with the same hydrophilicity, hydrophibicity and aromaticity.

cond-mat.soft↗
arXiv2021

Quantifying entropy production in active fluctuations of the hair-cell bundle from time irreversibility and uncertainty relations

We introduce lower bounds for the rate of entropy production of an active stochastic process by quantifying the irreversibility of stochastic traces obtained from mesoscopic degrees of freedom. Our measures of irreversibility reveal signatures of time's arrow and provide bounds for entropy production even in the case of active fluctuations that have no drift. We apply these irreversibility measures to experimental recordings of spontaneous hair-bundle oscillations in mechanosensory hair cells from the ear of the bullfrog. By analysing the fluctuations of only the tip position of hair bundles, we reveal irreversibility in active oscillations and estimate an associated rate of entropy production of at least $\sim 3 k_{\rm B}$/s, on average. Applying thermodynamic uncertainty relations, we predict that measuring both the tip position of the hair bundle and the mechano-electrical transduction current that enters the hair cell leads to tighter lower bounds for the rate of entropy production, up to $\sim 10^3 k_{\rm B}$/s in the oscillatory regime.

cond-mat.stat-mech↗
arXiv2021

Thermodynamics of Gambling Demons

We introduce and realize demons that follow a customary gambling strategy to stop a nonequilibrium process at stochastic times. We derive second-law-like inequalities for the average work done in the presence of gambling, and universal stopping-time fluctuation relations for classical and quantum non-stationary stochastic processes. We test experimentally our results in a single-electron box, where an electrostatic potential drives the dynamics of individual electrons tunneling into a metallic island. We also discuss the role of coherence in gambling demons measuring quantum jump trajectories.

cond-mat.stat-mech↗
arXiv2020

Controlling particle currents with evaporation and resetting from an interval

We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the appearance of a Brownian yet non-Gaussian diffusion: at long times, the particle distribution is non-Gaussian but its variance grows linearly in time. Moreover, we show that the effective diffusion coefficient of the particles in such systems is bounded from below by $(1-2/π)$ times their bare diffusion coefficient. For periodic boundary conditions, i.e., for diffusion on a ring with resetting, we demonstrate a "gauge invariance" of the spatial particle distribution for different choices of the resetting probability currents, in both stationary and non-stationary regimes. Finally, we apply our findings to a stochastic biophysical model for the motion of RNA polymerases during transcriptional pauses, deriving analytically the distribution of the length of cleaved RNA transcripts and the efficiency of RNA cleavage in backtrack recovery.

cond-mat.stat-mech↗
arXiv2020

Energetics of critical oscillators in active bacterial baths

We investigate the nonequilibrium energetics near a critical point of a non-linear driven oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power $\langle\dot{W}\rangle\sim (D_{\rm a}/τ)^{1/4}$ where $D_{\rm a}$ is the effective diffusivity and $τ$ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average stationary power and the variance of the work both below and above the saddle-node bifurcation. Above the bifurcation, the average power attains an optimal, minimum value for finite $τ$ that is below its zero-temperature limit. Furthermore, we reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below $2k_{\rm B}T_{\rm eff}$, with $T_{\rm eff}$ the effective temperature of the oscillator in the bacterial bath. We analyze different Markovian approximations to describe the nonequilibrium stationary state of the system. Finally, we illustrate our results in the experimental context by considering the example of driven colloidal particles in periodic optical potentials within an E. Coli bacterial bath.

cond-mat.soft↗
arXiv2020

Stochastic resetting antiviral therapies prevents drug resistance development

We study minimal mean-field models of viral drug resistance development in which the efficacy of a therapy is described by a one-dimensional stochastic resetting process with mixed reflecting-absorbing boundary conditions. We derive analytical expressions for the mean survival time for the virus to develop complete resistance to the drug. We show that the optimal therapy resetting rates that achieve a minimum and maximum mean survival times undergo a second and first-order phase transition-like behaviour as a function of the therapy efficacy drift. We illustrate our results with simulations of a population-dynamics model of HIV-1 infection.

cond-mat.stat-mech↗
arXiv2020

Extreme-Value Statistics of Stochastic Transport Processes: Applications to Molecular Motors and Sports

We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in molecular motor motion along linear filaments. Our results generalize the infimum law for entropy production and reveal a symmetry of the distribution of its maxima and minima. We also show that the relaxation spectrum of the full generating function, and hence of any moment, of the finite-time extrema distributions can be written in terms of the Mar{č}enko-Pastur distribution of random-matrix theory. Using this result, we obtain estimates for the extreme-value statistics of stochastic transport from the eigenvalue distributions of suitable Wishart and Laguerre random matrices. We confirm our results by numerical simulations of stochastic models of molecular motors and discuss as illustrative example our theory in the context of sports.

cond-mat.stat-mech↗
arXiv2020

Optimal Work Extraction and the Minimum Description Length Principle

We discuss work extraction from classical information engines (e.g., Szilárd) with $N$-particles, $q$ partitions, and initial arbitrary non-equilibrium states. In particular, we focus on their {\em optimal} behaviour, which includes the measurement of a set of quantities $Φ$ with a feedback protocol that extracts the maximal average amount of work. We show that the optimal non-equilibrium state to which the engine should be driven before the measurement is given by the normalised maximum-likelihood probability distribution of a statistical model that admits $Φ$ as sufficient statistics. Furthermore, we show that the minimax universal code redundancy $\mathcal{R}^*$ associated to this model, provides an upper bound to the work that the demon can extract on average from the cycle, in units of $k_{\rm B}T$. We also find that, in the limit of $N$ large, the maximum average extracted work cannot exceed $H[Φ]/2$, i.e. one half times the Shannon entropy of the measurement. Our results establish a connection between optimal work extraction in stochastic thermodynamics and optimal universal data compression, providing design principles for optimal information engines. In particular, they suggest that: (i) optimal coding is thermodynamically efficient, and (ii) it is essential to drive the system into a critical state in order to achieve optimal performance.

cond-mat.stat-mech↗
arXiv2020

First-passage Fingerprints of Water Diffusion near Glutamine Surfaces

The extent to which biological interfaces affect the dynamics of water plays a key role in the exchange of matter and chemical interactions that are essential for life. The density and the mobility of water molecules depend on their proximity to biological interfaces and can play an important role in processes such as protein folding and aggregation. In this work, we study the dynamics of water near glutamine surfaces---a system of interest in studies of neurodegenerative diseases. Combining molecular-dynamics simulations and stochastic modelling, we study how the mean first-passage time and related statistics of water molecules escaping subnanometer-sized regions vary from the interface to the bulk. Our analysis reveals a dynamical complexity that reflects underlying chemical and geometrical properties of the glutamine surfaces. From the first-passage time statistics of water molecules, we infer their space-dependent diffusion coefficient in directions normal to the surfaces. Interestingly, our results suggest that the mobility of water varies over a longer length scale than the chemical potential associated with the water-protein interactions. The synergy of molecular dynamics and first-passage techniques opens the possibility for extracting space-dependent diffusion coefficients in more complex, inhomogeneous environments that are commonplace in living matter.

cond-mat.stat-mech↗
arXiv2019

Exact Distributions of Currents and Frenesy for Markov Bridges

We consider discrete-time Markov bridges, chains whose initial and final states coincide. We derive exact finite-time formulae for the joint probability distributions of additive functionals of trajectories. We apply our theory to time-integrated currents and frenesy of enzymatic reactions, which may include absolutely irreversible transitions. We discuss the information that frenesy carries about the currents and show that bridges may violate known uncertainty relations in certain cases. Numerical simulations are in perfect agreement with our theory.

cond-mat.stat-mech↗