arXiv subjects

Andre C. Barato

Publications and source records attributed to Andre C. Barato.

At least 19 recordsLinked to original sources

arXiv2026

Cramer-Rao Inequality Generalizes the Equilibrium Energy Fluctuation-Response Relation to Nonequilibrium Steady States

Equilibrium steady states are fully characterized by the Boltzmann distribution, which depends only on the energy and the temperature. In contrast, nonequilibrium steady states, which describe a wide range of physical and biological phenomena, are generically much more complex, and their stationary distributions can depend on a zoo of kinetic parameters. A central challenge of nonequilibrium statistical mechanics is the identification of universal relations that hold for nonequilibrium steady states despite this complexity. We show here that a form of the Cramer-Rao inequality applies to arbitrary nonequilibrium steady-state distributions and contains no explicit dependence on kinetic parameters. A main original feature in our observation is that this inequality becomes a well-known fluctuation-response relation in equilibrium. The inequality involves three well-defined quantities: the fluctuations of the energy, the response given by the derivative of the average energy with respect to the inverse temperature, and the Fisher information with respect to the inverse temperature. We illustrate this inequality using three representative models: an active particle in a harmonic potential, a simple scheme for kinetic proofreading, and a one-dimensional model for heat conduction between two baths.

cond-mat.stat-mech↗

arXiv2026

Cyclic Heat Engine with the Ising model: role of interactions and criticality

Heat engines that convert thermal energy into work are a cornerstone of classical thermodynamics and remain an active area of contemporary research. Notable examples include microscopic heat engines, trade-off relations between power and efficiency, and the attainability of Carnot efficiency at finite power. We propose a cyclic heat engine based on the Ising model, in which the thermodynamic cycle involves variations of both temperature and magnetic field. We analyze the one-dimensional and mean-field Ising models, which allow for simple analytical results and provide new insight into the role of interactions in cyclic heat engines. In particular, we show that interactions can enhance both power and efficiency. Moreover, a system that does not operate as an engine in the absence of interactions can become an engine upon tuning the interaction strength. The mean-field model enables us to investigate the relevance of the phase transition for the performance of this Ising heat engine. Owing to the emergence of spontaneous magnetization, the mean-field model can still operate as an engine even when one of the magnetic fields is set to zero. Remarkably, when the work is maximized, we find that the optimal parameters are numerically consistent with this regime, in which one magnetic field vanishes and the cycle explores the phase transition. We also consider an alternative cycle for the mean-field model, obtained by varying the interaction strength while keeping both temperatures below the critical temperature and setting the magnetic field to zero throughout the cycle. The power and efficiency of this cycle are analyzed as well. Finally, while our analytical results are valid for the limit of large period we use numerical simulations for finite periods and show that the power decreases monotonically with the period.

cond-mat.stat-mech↗

arXiv2024

Inference of entropy production for periodically driven systems

The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is restricted to the case of nonequilibrium steady states driven by a fixed thermodynamic force. Based on a recent method that has been proposed for nonequilibrium steady states, we obtain an estimate of the entropy production based on the statistics of visible transitions and their waiting times for the case of periodically driven systems. The time-dependence of transition rates in periodically driven systems produces several differences in relation to steady states, which is reflected in the entropy production estimation. More specifically, we propose an estimate that does depend on the time between transitions but is independent of the specific time of the first transition, thus it does not require tracking the protocol. Formally, this elimination of the time-dependence of the first transition leads to an extra term in the inequality that involves the rate of entropy production and its estimate. We analyze a simple model of a molecular pump to understand the relation between the performance of the method and physical quantities such as energies, energy barriers, and thermodynamic affinity. Our results with this model indicate that the emergence of net motion in the form of a probability current in the space of states is a necessary condition for a relevant estimate of the rate of entropy production.

cond-mat.stat-mech↗

arXiv2022

Universal minimal cost of coherent biochemical oscillations

Biochemical clocks are essential for virtually all living systems. A biochemical clock that is isolated from an external periodic signal and subjected to fluctuations can oscillate coherently only for a finite number of oscillations. Furthermore, such an autonomous clock can oscillate only if it consumes free energy. What is the minimum amount of free energy consumption required for a certain number of coherent oscillations? We conjecture a universal bound that answers this question. A system that oscillates coherently for $\mathcal{N}$ oscillations has a minimal free energy cost per oscillation of $4π^2\mathcal{N} k_B T$. Our bound is valid for general finite Markov processes, is conjectured based on extensive numerical evidence, is illustrated with numerical simulations of a known model for a biochemical oscillator, and applies to existing experimental data.

cond-mat.stat-mech↗

arXiv2020

Stochastic discrete time crystals: Entropy production and subharmonic synchronization

Discrete time crystals are periodically driven systems that display spontaneous symmetry breaking of time translation invariance in the form of indefinite subharmonic oscillations. We introduce a thermodynamically consistent model for a discrete time crystal and analyze it using the framework of stochastic thermodynamics. In particular, we evaluate the rate of energy dissipation of this many body system of interacting noisy subharmonic oscillators in contact with a heat bath. Our model displays the novel phenomena of subharmonic synchronization, which corresponds to collective subharmonic oscillations of the individual units.

cond-mat.stat-mech↗

arXiv2019

Subharmonic oscillations in stochastic systems under periodic driving

Subharmonic response is a well known phenomena in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics due to thermal fluctuations. In contrast to stochastic autonomous systems in a stationary state, for which the number of coherent oscillations is fundamentally bounded by the number of states in the underlying network, we demonstrate that in periodically driven systems, subharmonic oscillations can, in principle, remain coherent forever, even in networks with a small number of states. We also show that, {\sl inter alia}, the thermodynamic cost rises only logarithmically with the number of coherent oscillations in a model calculation and that the possible periods of the persistent subharmonic response grow linearly with the number of states. We argue that our results can be relevant for biochemical oscillations and for stochastic models of time-crystals.

cond-mat.stat-mech↗

arXiv2018

Phase transition in thermodynamically consistent biochemical oscillators

Biochemical oscillations are ubiquitous in living organisms. In an autonomous system, not influenced by an external signal, they can only occur out of equilibrium. We show that they emerge through a generic nonequilibrium phase transition, with a characteristic qualitative behavior at criticality. The control parameter is the thermodynamic force, which must be above a certain threshold for the onset of biochemical oscillations. This critical behavior is characterized by the thermodynamic flux associated with the thermodynamic force, its diffusion coefficient, and the stationary distribution of the oscillating chemical species. We discuss metrics for the precision of biochemical oscillations by comparing two observables, the Fano factor associated with the thermodynamic flux and the number of coherent oscillations. Since the Fano factor can be small even when there are no biochemical oscillations, we argue that the number of coherent oscillations is more appropriate to quantify the precision of biochemical oscillations. Our results are obtained with three thermodynamically consistent versions of known models: the Brusselator, the activator-inhibitor model, and a model for KaiC oscillations.

cond-mat.stat-mech↗

arXiv2018

Arcsine Laws in Stochastic Thermodynamics

We show that the fraction of time a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by Lévy for Brownian motion. Stochastic currents with long streaks above or below their average are much more likely than those that spend similar fractions of time above and below their average. Our result is confirmed with experimental data from a Brownian Carnot engine. We also conjecture that two other random times associated with currents obey the arcsine law: the time a current reaches its maximum value and the last time a current crosses its average value. These results apply to, inter alia, molecular motors, quantum dots and colloidal systems.

cond-mat.stat-mech↗

arXiv2017

Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes

Periodic driving is used to operate machines that go from standard macroscopic engines to small non-equilibrium micro-sized systems. Two classes of such systems are small heat engines driven by periodic temperature variations and molecular pumps driven by external stimuli. Well known results that are valid for nonequilibrium steady states of systems driven by fixed thermodynamic forces, instead of an external periodic driving, have been generalized to periodically driven heat engines only recently. These results include a general expression for entropy production in terms of currents and affinities and symmetry relations for the Onsager coefficients from linear response theory. For nonequilibrium steady states, the Onsager reciprocity relations can be obtained from the more general fluctuation theorem for the currents. We prove a fluctuation theorem for the currents for periodically driven systems. We show that this fluctuation theorem implies a fluctuation dissipation relation, symmetry relations for Onsager coefficients and further relations for nonlinear response coefficients. The setup in this paper is more general than previous studies, i.e., our results are valid for both heat engines and molecular pumps. The external protocol is assumed to be stochastic in our framework, which leads to a particularly convenient way to treat periodically driven systems.

cond-mat.stat-mech↗

arXiv2017

Dispersion of the time spent in a state: General expression for unicyclic model and dissipation-less precision

We compare the relation between dispersion and dissipation for two random variables that can be used to characterize the precision of a Brownian clock. The first random variable is the current between states. In this case, a certain precision requires a minimal energetic cost determined by a known thermodynamic uncertainty relation. We introduce a second random variable that is a certain linear combination of two random variables, each of which is the time a stochastic trajectory spends in a state. Whereas the first moment of this random variable is equal to the average probability current, its dispersion is generally different from the dispersion associated with the current. Remarkably, for this second random variable a certain precision can be obtained with an arbitrarily low energy dissipation, in contrast to the thermodynamic uncertainty relation for the current. As a main technical achievement, we provide an exact expression for the dispersion related to the time that a stochastic trajectory spends in a cluster of states for a general unicyclic network.

cond-mat.stat-mech↗

arXiv2017

Thermodynamic cost of external control

Artificial molecular machines are often driven by the periodic variation of an external parameter. This external control exerts work on the system of which a part can be extracted as output if the system runs against an applied load. Usually, the thermodynamic cost of the process that generates the external control is ignored. Here, we derive a refined second law for such small machines that include this cost, which is, for example, generated by free energy consumption of a chemical reaction that modifies the energy landscape for such a machine. In the limit of irreversible control, this refined second law becomes the standard one. Beyond this ideal limiting case, our analysis shows that due to a new entropic term unexpected regimes can occur: The control work can be smaller than the extracted work and the work required to generate the control can be smaller than this control work. Our general inequalities are illustrated by a paradigmatic three-state system.

cond-mat.stat-mech↗

arXiv2017

Universal bound on the efficiency of molecular motors

The thermodynamic uncertainty relation provides an inequality relating any mean current, the associated dispersion and the entropy production rate for arbitrary non-equilibrium steady states. Applying it here to a general model of a molecular motor running against an external force or torque, we show that the thermodynamic efficiency of such motors is universally bounded by an expression involving only experimentally accessible quantities. For motors pulling cargo through a viscous fluid, a universal bound for the corresponding Stokes efficiency follows as a variant. A similar result holds if mechanical force is used to synthesize molecules of high chemical potential. Crucially, no knowledge of the detailed underlying mechano-chemical mechanism is required for applying these bounds.

cond-mat.stat-mech↗

arXiv2016

Affinity- and topology-dependent bound on current fluctuations

We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system into a non-equilibrium steady state, and the topology of the network. The proof is based on a decomposition of the network into independent cycles with both positive affinity and positive stationary cycle current. This formalism allows for a refinement of the bound for systems in equilibrium or with locally vanishing affinities.

cond-mat.stat-mech↗

arXiv2016

Universal bounds on current fluctuations

For current fluctuations in non-equilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a new general class of constraints for nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2016

Sensory capacity: an information theoretical measure of the performance of a sensor

For a general sensory system following an external stochastic signal, we introduce the sensory capacity. This quantity characterizes the performance of a sensor: sensory capacity is maximal if the instantaneous state of the sensor has as much information about a signal as the whole time-series of the sensor. We show that adding a memory to the sensor increases the sensory capacity. This increase quantifies the improvement of the sensor with the addition of the memory. Our results are obtained with the framework of stochastic thermodynamics of bipartite systems, which allows for the definition of an efficiency that relates the rate with which the sensor learns about the signal with the energy dissipated by the sensor, which is given by the thermodynamic entropy production. We demonstrate a general tradeoff between sensory capacity and efficiency: if the sensory capacity is equal to its maximum 1, then the efficiency must be less than 1/2. As a physical realization of a sensor we consider a two component cellular network estimating a fluctuating external ligand concentration as signal. This model leads to coupled linear Langevin equations that allow us to obtain explicit analytical results.

cond-mat.stat-mech↗

arXiv2015

Dispersion for Two Classes of Random Variables: General Theory and Application to Inference of an External Ligand Concentration by a Cell

We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables like current and activity pertain to the first class, which is composed by random variables that change whenever a jump in the stochastic trajectory occurs. The second class corresponds to the time the trajectory spends in a state (or cluster of states). While the expression for the first class follows straightforwardly from known results in the literature, we show that a similar formalism can be used to derive an expression for the second class. As an application, we use this formalism to analyze a cellular two-component network estimating an external ligand concentration. The uncertainty related to this external concentration is calculated by monitoring different random variables related to an internal protein. We show that, inter alia, monitoring the time spent in the phosphorylated state of the protein leads to a finite uncertainty only if there is dissipation, whereas the uncertainty obtained from the activity of the transitions of the internal protein can reach the Berg and Purcell limit even in equilibrium.

cond-mat.stat-mech↗

arXiv2015

Skewness and Kurtosis in Statistical Kinetics

We obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to a well known lower bound on the randomness parameter, the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network. Our results demonstrate that evaluating these higher order moments with single molecule data can lead to information about the enzymatic scheme that is not contained in the randomness parameter.

physics.bio-ph↗

arXiv2015

A formal view on 2.5 large deviations and fluctuation relations

We obtain the rate function for the level 2.5 of large deviations for pure jump and diffusion processes. This result is proved by two methods: tilting, for which a tilted process with an appropriate typical behavior is considered, and a spectral method, for which the scaled cumulant generating function is used. We also briefly discuss fluctuation relations, pointing out their connection with large deviations at the level 2.5.

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