arXiv subjects

Massimiliano Esposito

Publications and source records attributed to Massimiliano Esposito.

At least 55 records · Page 3Linked to original sources

arXiv2025

Small-amplitude synchronisation in driven Potts models

We study driven $q$-state Potts models with thermodynamically consistent dynamics and global coupling. For a wide range of parameters, these models exhibit a dynamical phase transition from decoherent oscillations into a synchronised phase. Starting from a general microscopic dynamics for individual oscillators, we derive the normal form of the high-dimensional Hopf-Bifurcation that underlies the phase transition. The normal-form equations are exact in the thermodynamic limit and close to the bifurcation. Exploiting the symmetry of the model, we solve these equations and thus uncover the intricate stable synchronisation patterns of driven Potts models, characterised by a rich phase diagram. Making use of thermodynamic consistency, we show that synchronisation reduces dissipation in such a way that the most stable synchronised states dissipate the least entropy. Close to the phase transition, our findings condense into a linear dissipation-stability relation that connects entropy production with phase-space contraction, a stability measure. At finite system size, our findings suggest a minimum-dissipation principle for driven Potts models that holds arbitrarily far from equilibrium.

cond-mat.stat-mech↗

arXiv2025

Minimum-dissipation principle for synchronised stochastic oscillators far from equilibrium

We prove a linear stability-dissipation relation (SDR) for $q$-state Potts models driven far from equilibrium by a nonconservative force. At a critical coupling strength, these models exhibit a synchronisation transition from a decoherent into a synchronised state. In the vicinity of this transition, the SDR connects the entropy production rate per oscillator to the phase-space contraction rate, a measure of stability, in a simple way. For large but finite systems, we argue that the SDR implies a minimum-dissipation principle for driven Potts models as the dynamics selects stable non-equilibrium states with least dissipation. This principle holds arbitrarily far from equilibrium, for any stochastic dynamics, and for all $q$.

cond-mat.stat-mech↗

arXiv2025

Thermodynamics of coherent energy exchanges between lasers and two-level systems

We study the quantum thermodynamics of a coherent macroscopic electromagnetic field (laser) coupled to a two-level system (qubit) near resonance, from weak to strong driving regimes. This combined system is, in turn, weakly coupled to a thermal radiation field, and can be described by an autonomous quantum master equation. We show that the laser acts as an autonomous work source and that, in the macroscopic limit, the work produced is independent of the phase of the laser. Using the dressed qubit approach, we show that the variation of energy in the laser is not the work transferred to the dressed qubit, which is instead obtained from the ''dressed laser'' -- a coherent superposition of the laser and the qubit. Using a two-point measurement technique with counting fields, we obtain the full counting statistics for the work of the laser and dressed laser, and show that they satisfy Crooks fluctuation theorems. We then use these theorems as criteria to investigate the thermodynamic consistency of quantum master equations, first in the autonomous setup for the combined system, then in the non-autonomous setup where the coherent field is eliminated and effectively described by a time dependent external field. Treating the laser as an external field in known to yield expressions for the work which are in contradiction with quantum thermodynamics predictions in the strong drive regime. We show that these inconsistencies stem from a confusion between the laser and dressed laser, and show how to correct them. We also derive a new master equation, thermodynamically consistent at all driving regimes, from which the Bloch and Floquet master equations can be obtained using additional approximations (of which we also examine the consistency).

quant-ph↗

arXiv2024

Information thermodynamics for Markov jump processes coupled to underdamped diffusion: Application to nanoelectromechanics

We extend the principles of information thermodynamics to study energy and information exchanges between coupled systems composed of one part undergoing a Markov jump process and another underdamped diffusion. We derive integral fluctuation theorems for the partial entropy production of each subsystem and analyze two distinct regimes. First, when the inertial dynamics is slow compared to the discrete-state transitions, we show that the steady-state energy and information flows vanish at the leading order in an adiabatic approximation, if the underdamped subsystem is governed purely by conservative forces. To capture the non-zero contributions, we consistently derive dynamical equations valid to higher order. Second, in the limit of infinite mass, the underdamped dynamics becomes a deterministic Hamiltonian dynamics driving the jump processes, we capture the next-order correction beyond this limit. We apply our framework to study self-oscillations in the single-electron shuttle - a nanoelectromechanical system (NEMS) - from a measurement-feedback perspective. We find that energy flows dominate over information flows in the self-oscillating regime, and study the efficiency with which this NEMS converts electrical work into mechanical oscillations.

cond-mat.stat-mech↗

arXiv2024

Open-system eigenstate thermalization in a noninteracting integrable model

Significant attention has been devoted to the problem of thermalization of observables in isolated quantum setups by individual eigenstates. Here, we address this issue from an open quantum system perspective, examining an isolated setup where a small system (specifically, a single fermionic level) is coupled to a macroscopic fermionic bath. We argue that in such a model, despite its full integrability, the system observables exhibit thermalization when the system-bath setup resides in a typical eigenstate of its Hamiltonian, a phenomenon known as weak eigenstate thermalization. This thermalization occurs unless it is suppressed by localization due to strong coupling. We further show that following the quench of the system Hamiltonian, the system occupancy typically relaxes to the thermal value corresponding to the new Hamiltonian. Finally, we demonstrate that system thermalization also arises when the system is coupled to a bath that has been initialized in a typical eigenstate of its Hamiltonian. Our findings suggest that nonintegrability is not the sole driver of thermalization, highlighting the need for complementary approaches to fully understand the emergence of statistical mechanics.

quant-ph↗

arXiv2024

Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization

We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena such as liquid-liquid phase separation, coacervation, and the formation of biomolecular condensates.

q-bio.MN↗

arXiv2024

Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling

There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior. We clarify this issue by employing large deviation theory. We distinguish two distinct classes of discontinuous phase transitions that have different dynamical properties. The first class is associated with phase coexistence, i.e., the presence of multiple stable attractors of the system dynamics (e.g., local minima of the free energy functional) in a finite phase diagram region around the phase transition point. In that case, one observes asymptotic exponential scaling related to stochastic switching between attractors (though the onset of exponential scaling may sometimes occur for very large system sizes). In the second class, there is no phase coexistence away from the phase transition point, while at the phase transition point itself there are infinitely many attractors. In that case, one observes power-law scaling related to the diffusive nature of the system relaxation to the stationary state.

cond-mat.stat-mech↗

arXiv2024

Bridging Freidlin-Wentzell large deviations theory and stochastic thermodynamics

For overdamped Langevin systems subjected to weak thermal noise and nonconservative forces, we establish a connection between Freidlin-Wentzell large deviations theory and stochastic thermodynamics. First, we derive a series expansion of the quasipotential around the detailed-balance solution, i.e. the system's free energy, and identify the condition for the linear response regime to hold even far from equilibrium. Second, we prove that the escape rate from dissipative fixed points of the macroscopic dynamics is bounded by the entropy production of trajectories that relax into, and escape from the attractors. These results provide the foundation to study the nonequilibrium thermodynamics of dissipative metastable states.

cond-mat.stat-mech↗

arXiv2024

General Theory of Static Response for Markov Jump Processes

We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they are constrained by the graph topology (i.e. the incidence matrix) by deriving response relations (i.e. linear constraints linking the different responses) and topology-dependent bounds. For unicyclic networks, all scaled current responses are between zero and one and must sum to one. Applying these results to stochastic thermodynamics, we derive explicit expressions for the static response of fundamental currents (which carry the full dissipation) to fundamental thermodynamic forces (which drive the system away from equilibrium).

cond-mat.stat-mech↗

arXiv2024

Dissipation bounds precision of current response to kinetic perturbations

The precision of currents in Markov networks is bounded by dissipation via the so-called thermodynamic uncertainty relation (TUR). In our work, we demonstrate a similar inequality that bounds the precision of the static current response to perturbations of kinetic barriers. Perturbations of such type, which affect only the system kinetics but not the thermodynamic forces, are highly important in biochemistry and nanoelectronics. We prove that our inequality cannot be derived from the standard TUR. Instead, it implies the standard TUR and provides an even tighter bound for dissipation. We also provide a procedure for obtaining the optimal response precision for a given model.

cond-mat.stat-mech↗

arXiv2024

Dissipation in Hydrodynamics from Micro- to Macroscale: Wisdom from Boltzmann and Stochastic Thermodynamics

We show that macroscopic irreversible thermodynamics for viscous fluids can be derived from exact information-theoretic thermodynamic identities valid at the microscale. Entropy production, in particular, is a measure of the loss of many-particle correlations in the same way in which it measures the loss of system-reservoirs correlations in stochastic thermodynamics (ST). More specifically, we first show that boundary conditions at the macroscopic level define a natural decomposition of the entropy production rate (EPR) in terms of thermodynamic forces multiplying their conjugate currents, as well as a change in suitable nonequilibrium potential that acts as a Lyapunov function in the absence of forces. Moving to the microscale, we identify the exact identities at the origin of these dissipative contributions for isolated Hamiltonian systems. We then show that the molecular chaos hypothesis, which gives rise to the Boltzmann equation at the mesoscale, leads to a positive rate of loss of many-particle correlations, which we identify with the Boltzmann EPR. By generalizing the Boltzmann equation to account for boundaries with nonuniform temperature and nonzero velocity, and resorting to the Chapman-Enskog expansion, we recover the macroscopic theory we started from. Finally, using a linearized Boltzmann equation we derive ST for dilute particles in a weakly out-of-equilibrium fluid and its corresponding macroscopic thermodynamics. Our work unambiguously demonstrates the information-theoretical origin of thermodynamic notions of entropy and dissipation in macroscale irreversible thermodynamics.

cond-mat.stat-mech↗

arXiv2024

Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization

Based on exact integration of the Schrödinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scales, including the nonequilibrium steady state regime and the final stage of global thermalization. We find that the entropy production is dominated for most times by microscopic deviations from thermality in the baths and the correlation between (but not inside) the baths. Despite these microscopic deviations from thermality, the temperatures and chemical potentials of the baths thermalize as expected, even though our model is integrable. Importantly, this observation is confirmed for both initially mixed and pure states. We further observe that the bath-bath correlations are quite insensitive to the system-bath coupling strength contrary to intuition. Finally, the system-bath correlation, small in an absolute sense, dominates in a relative sense and displays pure quantum correlations for all studied parameter regimes.

cond-mat.stat-mech↗

arXiv2024

Symmetry shapes thermodynamics of macroscopic quantum systems

We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We apply our technique to generic $N$ identical interacting $d$-level quantum systems. Using permutation invariance, we find that, for large $N$, entropy displays a universal large deviation behavior with a rate function $s(\boldsymbol{x})$ that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group $\text{S}_N$. In turn, the partition function is shown to satisfy a large deviation principle with a free energy $f(\boldsymbol{x})=e(\boldsymbol{x})-β^{-1}s(\boldsymbol{x})$, where $e(\boldsymbol{x})$ is a rate function that only depends on the ground state energy of particular subspaces determined by group representation theory. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations.

quant-ph↗

arXiv2024

Thermodynamic cost of precise timekeeping in an electronic underdamped clock

Clocks are inherently out-of-equilibrium because, due to friction, they constantly consume free energy to keep track of time. The Thermodynamic Uncertainty Relation (TUR) quantifies the trade-off between the precision of any time-antisymmetric observable and entropy production. In the context of clocks, the TUR implies that a minimum entropy production is needed in order to achieve a certain level of precision in timekeeping. But the TUR has only been proven for overdamped systems. Recently, a toy model of a classical underdamped pendulum clock was proposed that violated this relation (Phys. Rev. Lett. 128, 130606), thus demonstrating that the TUR does not hold for underdamped dynamics. We propose an electronic implementation of such a clock, using a resistor-inductor-capacitor (RLC) circuit and a biased CMOS inverter (NOT gate), which can work at different scales. We find that in the nanoscopic single-electron regime of the circuit, we essentially recover the toy model violating the TUR bound. However, in different macroscopic regimes of the circuit, we show that the TUR bound is restored and analyze the thermodynamic efficiency of timekeeping.

cond-mat.stat-mech↗

arXiv2024

System-bath entanglement of noninteracting fermionic impurities: Equilibrium, transient, and steady-state regimes

We investigate the behavior of entanglement between a single fermionic level and a fermionic bath in three distinct thermodynamic regimes. First, in thermal equilibrium, we analyze the dependence of entanglement on the considered statistical ensemble: for the grand canonical state, it is generated only for a sufficiently strong system-bath coupling, whereas it is present for arbitrarily weak couplings for the canonical state with a fixed particle number. The threshold coupling strength, at which entanglement appears, is shown to strongly depend on the bath bandwidth. Second, we consider the relaxation to equilibrium. In this case a transient entanglement in a certain time interval can be observed even in the weak-coupling regime, when the reduced dynamics and thermodynamics of the system can be well described by an effectively classical and Markovian master equation for the state populations. At strong coupling strengths, entanglement is preserved for long times and converges to its equilibrium value. Finally, in voltage-driven junctions, a steady-state entanglement is generated for arbitrarily weak system-bath couplings at a certain threshold voltage. It is enhanced in the strong-coupling regime, and it is reduced by either the particle-hole or the tunnel coupling asymmetry.

quant-ph↗

arXiv2024

Methods and Conversations in (Post)Modern Thermodynamics

Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues.

cond-mat.stat-mech↗

arXiv2023

A chemical reaction network implementation of a Maxwell demon

We study an autonomous model of a Maxwell demon that works by rectifying thermal fluctuations of chemical reactions. It constitutes the chemical analog of a recently studied electronic demon. We characterize its scaling behavior in the macroscopic limit, its performances, and the impact of potential internal delays. We obtain analytical expressions for all quantities of interest, namely, the generated reverse chemical current, the output power, the transduction efficiency, and the correlations between the numbers of molecules. Due to a bound on the nonequilibrium response of its chemical reaction network, we find that, contrary to the electronic case, there is no way for the Maxwell demon to generate a finite output in the macroscopic limit. Finally, we analyze the information thermodynamics of the Maxwell demon from a bipartite perspective. In the limit of a fast demon, the information flow is obtained, its pattern in the state space is discussed, and the behavior of the partial efficiencies related to the measurement and the feedback processes is examined.

cond-mat.stat-mech↗

arXiv2023

Two-point measurement energy statistics from particle scattering

We show that the energy statistics resulting from a two-point measurement of an isolated quantum system subject to a time-dependent driving protocol can be probed by subjecting the same system to a collision with a suitably prepared incoming particle. This means that the particle acts both as an external drive and as an energy measurement device for the quantum system and that energy fluctuations can be defined within a fully autonomous setting.

quant-ph↗