arXiv subjects

Carlos E. Fiore

Publications and source records attributed to Carlos E. Fiore.

At least 19 recordsLinked to original sources

arXiv2026

Pareto-optimal control strategies in intrinsically nonequilibrium systems

Thermodynamic control is typically formulated as the optimisation of a single objective, yet competing costs rarely admit a common optimum, so single-objective control captures only one corner of the achievable performance space. We develop a general framework for multi-objective thermodynamic control of intrinsically nonequilibrium systems that maps out the full Pareto front of optimal control strategies. We show that Pareto-optimal protocols generically consist of smooth branches connected by boundary jumps, and that the relative weights of the objectives combine with the physical parameters into a single intrinsic scale that alone governs the trade-off. Remarkably, this scale plays a double role: it parametrizes a single functional form that generates the entire front, and it defines control equivalence classes, in which systems with different parameters but the same scale share identical optimal strategies. We illustrate the framework for two paradigmatic systems that are experimentally accessible: transport of an active particle in a harmonic trap, and a cyclic quantum-dot engine. For both, we obtain the Pareto front and optimal strategies in closed form.

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.

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arXiv2025

Universal splitting of phase transitions and performance optimization in driven collective systems

Spontaneous symmetry breaking is a hallmark of equilibrium systems, typically characterized by a single critical point separating ordered and disordered phases. Recently, a novel class of non-equilibrium phase transitions was uncovered [Phys. Rev. Res. {\bf 7}, L032049 (2025)], showing that the combined effects of simultaneous contact with thermal baths at different temperatures and external driving forces can split the conventional order-disorder transition into two distinct critical points, determined by which ordered state initially dominates. We show the robustness of this phenomenon by extending a minimal interacting-spin model from the idealized case of simultaneous bath coupling to a finite-time coupling protocol. In particular, we introduce two protocols in which the system interacts with a single bath at a time: a stochastic protocol, where the system randomly switches between the baths at different temperatures, and a deterministic protocol where the coupling alternates periodically. Our analysis reveals two key results: (i) the splitting of phase transitions persists across all coupling schemes -- simultaneous, stochastic, and deterministic -- and (ii) different optimizations of power and efficiency in a collectively operating heat engine reveal that both the stochastic and deterministic protocols exhibit superior global performance at intermediate switching rates and periods when compared to simultaneous coupling. The global trade-off between power and efficiency is described by an expression solely depending on the temperatures of thermal reservoirs as the efficiency approaches to the ideal limit.

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arXiv2025

Exact Mapping of Nonequilibrium to Equilibrium Phase Transitions for Systems in Contact with Two Thermal Baths

We show that a large class of nonequilibrium many-body systems in contact with two thermal baths admit an exact mapping onto equivalent equilibrium systems. This mapping provides direct access to nonequilibrium phase transition points from known equilibrium results, irrespective of the model, interaction topology, or distance from equilibrium. We verify the universality of this correspondence using paradigmatic models (Ising, Potts, and Blume-Capel), and highlight distinctive features in entropy production close to critical and tricritical points. Our findings connect equilibrium and nonequilibrium statistical mechanics, with implications for microscopic thermal machines and stochastic thermodynamics.

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arXiv2025

Emergent collective heat engines from neighborhood-dependent thermal reservoirs

We introduce and analyze a class of heat engines composed of interacting units, in which the thermal reservoir is associated with the neighborhood surrounding each unit. These systems can be mapped onto stochastic opinion models and are characterized by collective behavior at low temperatures, as well as different types of phase transitions, marked by spontaneous symmetry breaking and classifications that depend on topology and neighborhood. For the case of contact with two thermal baths, equivalent to each unit having $k = 4$ nearest neighbors, the system can be tuned to operate at maximum power without sacrificing efficiency or increasing dissipation. These quantities are related by the general expression $ \beta_2 {\cal P} \eta_c =-J_4 \eta \sigma$ when the worksource stems from different interaction energies. The heat engine placed in contact with more than three reservoirs is more revealing, showing that the intermediate thermal reservoir can be conveniently adjusted to achieve the desired compromise between power, efficiency, and dissipation. The influence of lattice topology (regular and random-regular networks), its relationship with collective operation as well as the distinct ratios between the temperatures of the thermal baths, has also been investigated.

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arXiv2025

Collective heat engines via different interactions: Minimal models, thermodynamics and phase transitions

We investigate the dynamics and thermodynamics of a framework composed of interacting units in which parameters (temperatures and energies) assume distinct values due to the contact with distinct (cold and hot) thermal reservoirs. The influence of different ingredients, such as the contact between thermal baths (simultaneous versus not simultaneous contact), the coupling between them (equal or different couplings) and the topology of interactions (all-to-all and local interactions) is investigated. Closed expressions for transition lines have been obtained, expressed by a linear combination of interaction energies times reciprocal temperatures for the simultaneous thermal contact baths and deviates from it when the contact is not simultaneous. The interplay between performance and dissipation is investigated under different conditions, giving rise to a richness of operation regimes, such as heat-engine and heat pump. The relationship between thermodynamic quantities (power, efficiency and dissipation) allows a careful choice of parameters to ensure the desirable compromise between them. Finally, the influence of different interactions energies (Ising, Potts versus Blume-Emery-Griffiths (BEG) like) are investigated, revealing that Potts interactions in general present superior performances than BEG ones.

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arXiv2025

Steady-state heat engines driven by finite reservoirs

We provide a consistent thermodynamic analysis of stochastic thermal engines driven by finite-size reservoirs, which are in turn coupled to infinite-size reservoirs. We consider a cyclic operation mode, where the working medium couples sequentially to hot and cold reservoirs, and a continuous mode with both reservoirs coupled simultaneously. We derive an effective temperature for the finite-size reservoirs determining the entropy production for two-state engines in the sequential coupling scenario, and show that finite-size reservoirs can meaningfully affect the power when compared to infinite-size reservoirs in both sequential and simultaneous coupling scenarios. We also investigate a three-state engine comprising two interacting units and optimize its performance in the presence of a finite reservoir. Notably, we show that the efficiency at maximum power can exceed the Curzon-Ahlborn bound with finite reservoirs. Our work introduces tools to optimize the performance of nanoscale engines under realistic conditions of finite reservoir heat capacity and imperfect thermal isolation.

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arXiv2025

Characterization and optimization of heat engines: Pareto-optimal fronts and universal features

Characterizing and optimizing nanoscopic heat engines require an appropriate understanding of the interplay between power, efficiency, entropy production and fluctuations. Despite significant recent advancements, including linear stochastic thermodynamics and thermodynamic uncertainty relations (TURs), a complete scenario remains elusive. In this work, we give a further step by showing that, under certain common and general conditions, the heat engine regime can be characterized by the minima of power fluctuations and entropy production, which together delimit its optimal performance, achieved when these conditions are fully satisfied. Conversely, when these conditions are not strictly met, the occurrence of the minimum still approximately describes the system, suggesting a broader range of applicability. Contrasting with most of studies in which the system optimization is carried out solely taking into account the power and efficiency, we introduce a multi-objective optimization framework based on Pareto fronts, also considering the role of fluctuation and dissipation. Our results reveal a general trend: while simultaneous optimization over a few parameters typically yields convex Pareto fronts, these fronts become concave as more parameters are varied freely and non-conservative driving becomes significant. Illustrating our findings, we consider simple two and three state systems as well as richer collective systems, exhibiting novel aspects of optimizations and protocol phase transitions.

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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.

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arXiv2024

Splitting of nonequilibrium phase transitions in driven Ising models

Spontaneous symmetry breaking occurs in various equilibrium and nonequilibrium systems, where phase transitions are typically marked by a single critical point that separates ordered and disordered regimes. We reveal a novel phenomenon in which the interplay between different temperatures and driving forces splits the order-disorder transition into two distinct transition points depending on which ordered state initially dominates. Crucially, these two emerging phases have distinct scaling behaviors and thermodynamic properties. To study this, we propose a minimal variant of the Ising model where spins are coupled to two thermal baths and subjected to two opposite driving forces associated to them. Our findings, robust both for all-to-all interactions (where exact solutions are possible) and nearest-neighbor couplings on a square lattice, uncover unique nonequilibrium behaviors and scaling laws for crucial thermodynamic quantities, such as efficiency, dissipation, power and its fluctuations, that are different between the two ordered phases. We also highlight that one of these emerging phases enables heat-engine operations that are less dissipative and show reduced fluctuations. In this setup, the system can also operate near maximum power and efficiency over a wide parameter range. Our results offer new insights into the relevance of phase transitions under nonequilibrium conditions.

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arXiv2024

Coherence resonance in influencer networks

Complex networks are abundant in nature and many share an important structural property: they contain a few nodes that are abnormally highly connected (hubs). Some of these hubs are called influencers because they couple strongly to the network and play fundamental dynamical and structural roles. Strikingly, despite the abundance of networks with influencers, little is known about their response to stochastic forcing. Here, for oscillatory dynamics on influencer networks, we show that subjecting influencers to an optimal intensity of noise can result in enhanced network synchronization. This new network dynamical effect, which we call coherence resonance in influencer networks, emerges from a synergy between network structure and stochasticity and is highly nonlinear, vanishing when the noise is too weak or too strong. Our results reveal that the influencer backbone can sharply increase the dynamical response in complex systems of coupled oscillators.

nlin.AO↗

arXiv2024

Thermodynamics of underdamped Brownian collisional engines: New insights and resonant phenomena

Collisional Brownian engines have been proposed as alternatives for nonequilibrium nanoscale engines. However, most studies have focused on the simpler overdamped case, leaving the role of inertia much less explored. In this work, we introduce the idea of collisional engines to underdamped Brownian particles, where each stage is sequentially subjected to a distinct driving force. A careful comparison between the performance of underdamped and overdamped Brownian work-to-work engines has been undertaken. The results show that underdamped Brownian engines generally outperform their overdamped counterparts. A key difference is the presence of a resonant regime in underdamped engines, in which both efficiency and power output are enhanced across a broad set of parameters. Our study highlights the importance of carefully selecting dynamics and driving protocols to achieve optimal engine performance.

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arXiv2024

Work statistics at first-passage times

We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterized by a first passage event that marks the completion of the non-equilibrium process. In particular, we consider a particle diffusing in one dimension in the presence of a time-dependent potential $U(x,t) = k |x-vt|^n/n$, where $k>0$ is the stiffness and $n>0$ is the order of the potential. Moreover, the particle is confined between two absorbing walls, located at $L_{\pm}(t) $, that move with a constant velocity $v$ and are initially located at $L_{\pm}(0) = \pm L$. As soon as the particle reaches any of the boundaries, the process is said to be completed and here, we compute the work done $W$ by the particle in the modulated trap upto this random time. Employing the Feynman-Kac path integral approach, we find that the typical values of the work scale with $L$ with a crucial dependence on the order $n$. While for $n>1$, we show that $\mom{W} \sim L^{1-n}~\exp \left[ \left( {k L^{n}}/{n}-v L \right)/D \right] $ for large $L$, we get an algebraic scaling of the form $\mom{W} \sim L^n$ for the $n<1$ case. The marginal case of $n=1$ is exactly solvable and our analysis unravels three distinct scaling behaviours: (i) $\mom{W} \sim L$ for $v>k$, (ii) $\mom{W} \sim L^2$ for $v=k$ and (iii) $\mom{W} \sim \exp\left[{-(v-k)L}\right]$ for $v<k$. For all cases, we also obtain the probability distribution associated with the typical values of $W$. Finally, we observe an interesting set of relations between the relative fluctuations of the work done and the first-passage time for different $n$ -- which we argue physically. Our results are well supported by the numerical simulations.

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arXiv2023

Thermodynamics of a minimal collective heat engine: Comparison between engine designs

Collective effects have attracted remarkable recent interest, not only for their presence in several systems in nature but also for the possibility of being used for the construction of efficient engine setups. Notwithstanding, little is known about the influence of the engine design and most studies are restricted to the simplest cases (e.g. simultaneous contact with two thermal baths), not necessarily constituting a realistic setup implementation. Aimed at partially filling this gap, we introduce the collisional/sequential description for a minimal model for collective effects, composed of two interacting nanomachines placed in contact with a distinct thermal reservoir and nonequilibrium worksource at each stage/stroke. Thermodynamic quantities are exactly obtained irrespectively the model details. Distinct kinds of engines are investigated and the influence of the interaction, temperature, period, and time asymmetry have been undertaken. Results show that a careful design of interaction provides a superior performance than the interactionless case, including optimal power outputs and efficiencies at maximum power greater than known bounds or even the system presenting efficiencies close to the ideal (Carnot) limit. We also show that the case of the system simultaneously placed in contact with two thermal reservoirs constitutes a particular case of our framework.

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arXiv2023

Entropy Production on Cooperative Opinion Dynamics

As one of the most widespread social dynamics, cooperative behavior is among the most fascinating collective phenomena. Several animal species, from social insects to human beings, feature social groups altruistically working for a common benefit. This collaborative conduct pervades the actions and opinions of individuals, yielding strategic decision-making between political, religious, ethnic, and economic social puzzles. Here, we explore how cooperative behavior phenomena impact collective opinion dynamics and entropy generation in social groups. We select a random fraction $f$ of community members as collaborative individuals and model the opinion dynamics using a social temperature parameter $q$ that functions as a social anxiety noise. With probability $q$, regular individuals oppose their companions about a social decision, assuming group dissent. Collaborative agents experience a reduced effective social noise $μq$, where $0 < μ< 1$ is the social anxiety noise sensibility parameter that enhances social validation. We perform numerical simulations and mean-field analysis and find the system undergoes nonequilibrium order-disorder phase transitions with expressive social entropy production. Our results also highlight the effects of an individual social anxiety attenuation level in enhancing group consensus and inducing exuberant collective phenomena in complex systems.

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arXiv2023

Thermodynamics of interacting systems: the role of the topology and collective effects

We will study a class of system composed of interacting unicyclic machines placed in contact with a hot and cold thermal baths subjected to a non-conservative driving worksource. Despite their simplicity, these models showcase an intricate array of phenomena, including pump and heat engine regimes as well as a discontinuous phase transition. We will look at three distinctive topologies: a minimal and beyond minimal (homogeneous and heterogeneous interaction structures). The former case is represented by stark different networks ("all-to-all" interactions and only a central interacting to its neighbors) and present exact solutions, whereas homogeneous and heterogeneous structures have been analyzed by numerical simulations. We find that the topology plays a major role on the thermodynamic performance for smaller values of individual energies, in part due to the presence of first-order phase-transitions.Contrariwise, the topology becomes less important as individual energies increases and results are well-described by a system with all-to-all interactions.

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arXiv2023

Powerful ordered collective heat engines

We introduce a class of stochastic engines in which the regime of units operating synchronously can boost the performance. Our approach encompasses a minimal setup composed of $N$ interacting units placed in contact with two thermal baths and subjected to a constant driving worksource. The interplay between unit synchronization and interaction leads to an efficiency at maximum power between the Carnot, $η_{c}$, and the Curzon-Ahlborn bound, $η_{CA}$. Moreover, these limits can be respectively saturated maximizing the efficiency, and by simultaneous optimization of power and efficiency. We show that the interplay between Ising-like interactions and a collective ordered regime is crucial to operate as a heat engine. The main system features are investigated by means of a linear analysis near equilibrium, and developing an effective discrete-state model that captures the effects of the synchronous phase. The present framework paves the way for the building of promising nonequilibrium thermal machines based on ordered structures.

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arXiv2023

Nonequilibrium thermodynamics of the majority vote model

The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. However, its original formulation is not, in general, thermodynamically consistent, precluding the achievement of quantities such as power and heat, as well as their behaviors at phase transition regimes. Here, we circumvent this limitation by introducing the idea of a distinct heat bath per local configuration, in such a way that each neighborhood value is associated with a distinct and well-defined thermal bath. Thermodynamic properties are derived for a generic majority vote model, irrespective of its neighborhood and lattice topology. The behavior of energy/heat fluxes at phase transitions, whether continuous or discontinuous, in regular and complex topologies, is investigated in detail. Unraveling the contribution of each local configuration explains the nature of the phase diagram and reveals how dissipation arises from the dynamics.

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