arXiv subjects

Massimiliano Esposito

Publications and source records attributed to Massimiliano Esposito.

At least 19 recordsLinked to original sources

arXiv2026

Quantum instanton approach to metastable collective spin systems: Numerical implementation and applications

Driven-dissipative collective spin systems can host several long-lived metastable states; rare switching between them governs slow relaxation and first-order dissipative phase transitions associated with changes in the dominant stationary state. In the companion Letter [arXiv:2604.15091], we introduced a quantum instanton framework based on exact quasiprobability dynamics to describe this switching and illustrated it with a minimal model possessing a simplifying symmetry. Here we develop its numerical implementation, combining collocation and shooting methods, and apply it to two microscopically motivated systems: the Lipkin-Meshkov-Glick model with purely collective dissipation and the cooperative resonance fluorescence with collective and local dissipation. By determining the leading exponential scaling of switching rates between metastable attractors, we predict the stationary magnetization, the first-order dissipative phase-transition point, and the exponential scaling of slow relaxation rates. These predictions agree with quantum master-equation calculations and an exact analytical result for the second model without dephasing. We also examine how the choice of quasiprobability representation affects numerical convergence and find that the alternative semiclassical Wigner approach, based on Gaussian truncation, has varying accuracy across models and parameter regimes. These results substantiate the framework's applicability to experimentally relevant collective spin systems with both collective and local dissipation.

quant-ph↗

arXiv2026

Physical limits to stochastic classifiers

Stochastic physical computers use random transitions between states to process inputs. We quantify their ability to solve distinct tasks as the control parameters of a device vary. For Markov jump devices, we bound the number of classification tasks attainable at a prescribed output margin, with each task defined as a binary labeling of fixed inputs. Combining geometric packing with fluctuation-response inequalities, we bound this number in terms of the control range and dimension, rate sensitivities, output fluctuations, and entropy production. For state and net-current observables, when controls change kinetics without changing thermodynamic forces and energies, the number of tasks is shaped by entropy production and output fluctuations. If the product of their maximum values over the allowed control settings and inputs is too small, the device can perform at most one task. An exactly solvable two-state switch illustrates how sufficient driving and observation time enable barrier tuning to select copying or inversion.

cond-mat.stat-mech↗

arXiv2026

Mutual linearity from classical response theory

We unify known mutual-linearity relations for Markov jump processes and chemical reaction networks within a common framework based on classical finite-response theory. In a Markov jump process, an exact finite-response identity shows that all stationary probability changes share a common factor when the rates of one edge change. Eliminating this factor gives the relations between probabilities, observables, and currents, even far from equilibrium. We also explain how the same argument applies when one coefficient of a linear system changes and recovers the known relations in Laplace space and between stationary complex activities in chemical reaction networks.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic efficiency of communication channels

We identify a broad class of communication channels that captures common physical constraints in both artificial and natural systems and derive bounds on their thermodynamic cost. We find that the entropy production per channel use is bounded from below by the input-output mutual information, and their ratio -mutual information divided by entropy production- defines the thermodynamic efficiency. Unlike previous studies of energy-constrained communication channels, our analysis shows that thermodynamic costs must be assigned not only to the input symbols themselves, but also to transitions between successive symbols. As a result, maximizing thermodynamic efficiency favors a biased input that switches only rarely, rather than the capacity-achieving input. For the binary symmetric channel, this preference emerges through a pitchfork bifurcation that spontaneously breaks the symmetry of the channel. A minimal model of cellular sensing exhibits the same phenomenon.

cond-mat.stat-mech↗

arXiv2026

Dynamical phase transitions for single particles in the semiclassical and weak noise limits

We present a unifying description of dynamical phase transitions in the unitary evolution of an isolated quantum particle and the dissipative relaxation of a classical Brownian particle, based on a dynamical generat- ing function. In the semiclassical and weak-noise limits, Fisher zeros of this function condense in the complex- time plane and reach the corresponding physical axes, producing dynamical phase transitions through a competition between return trajectories. This establishes a direct connection between quantum and classical (finite-time) dynamical phase transitions, where the semiclassical limit plays the role of the thermodynamic limit. In particular, the established link naturally provides a classical version of the Loschmidt amplitude and shows how dynamical quantum phase transitions, typically associated with isolated many-body systems, can arise in a single-particle quantum system. The dynamical phases are distinguished by a unifying, trajectory- based order parameter, realized as a classical correlation function and a sequential quantum weak value.

cond-mat.stat-mech↗

arXiv2026

A Minimal Thermodynamically Consistent Chemical Oscillator

Inspired by the chemical reaction network considered as the smallest system featuring a Hopf bifurcation and its reversible extension, we introduce an even more minimal reaction network that is thermodynamically consistent and exhibits autonomous oscillations under nonequilibrium driving. The model combines three features that are rarely realized simultaneously in compact oscillator networks: a chemically plausible structure restricted to uni- and bimolecular reactions, reversibility of such reactions, and analytical tractability. The system consists of three internal species coupled to two chemostatted species and still undergoes a supercritical Hopf bifurcation when a chemostat concentration is varied. To analyze the dynamics and thermodynamics near the onset of oscillations, we employ the mathematical technique of normal-form reduction, which allows obtaining a controlled irreversible approximation that preserves the leading phase-space structure of the full reversible network while enabling explicit calculations. This framework provides analytical access to the bifurcation structure and the leading contributions governing thermodynamic observables. Within this setting, we use the onset of oscillations to characterize the thermodynamic response of the system. In particular, we offer an analytical description of key thermodynamic quantities such as the semi-grand Gibbs free energy and the non-conservative work rate, which exhibit a kink-like discontinuity at the Hopf bifurcation. We thus provide an analytical description of a phenomenon previously characterized only through numerical simulations of more complex networks.

cond-mat.stat-mech↗

arXiv2026

Emergent Second Law for Time-Dependent Nonequilibrium States

For nonautonomous open systems described by macroscopic stochastic thermodynamics, we derive an emergent second law that constrains time-dependent macroscopic fluctuations by the entropy production along the most probable evolution under the time-reversed driving protocol. We show that this bound can be understood as a macroscopic consequence of the fluctuation theorem: the time reverse of this evolution provides a possible fluctuation path under the forward dynamics. In the linear-response and slow-driving regime, the bound becomes an equality to first order and generalizes the McLennan-Zubarev formula to the time-dependent probability density of nonautonomous systems with weak nonconservative affinities. We illustrate our results in a bistable system under sudden quenches and periodic driving.

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arXiv2026

Dynamical Fluctuation-Response Relations

We derive exact dynamical fluctuation-response relations (FRRs) for time-integrated observables of any nonautonomous Markov jump process. The finite-time covariance splits into an initial variability and an integral of response kernels along the driven dynamics. The identity sharpens the dynamical response thermodynamic and kinetic uncertainty relations and fluctuation-response inequalities (FRIs). For autonomous processes, dynamical FRRs yield two complementary frequency-domain relations. Steady-state FRRs are recovered in the long time limit, along with the fluctuation-dissipation theorem and Onsager reciprocity for detailed-balance dynamics. The importance of initial variability for slowly relaxing systems is also highlighted.

cond-mat.stat-mech↗

arXiv2026

Identifying Non-Ideal Reaction-Diffusion Systems Unable to Maintain Diffusion Out-of-Equilibrium

We develop a general method, based on the construction of a kinetic potential serving as a Lyapunov function, to establish when diffusion necessarily equilibrates in non-ideal reaction-diffusion systems under arbitrary driving by autonomous homogeneous chemostats. This equilibration of diffusion implies vanishing diffusion currents and homogeneous chemical potentials, while reactions can remain far from equilibrium. Using this method, we generalize the results of J. Chem. Phys. 161, 174108 (2024) by relaxing some of the underlying assumptions. Specifically, we show that diffusion equilibrates in reaction-diffusion systems whose chemical reaction network is either pseudo-detailed balanced, with reaction fluxes controlled by the stoichiometry of reactants and products, or complex balanced, with reaction fluxes controlled only by the stoichiometry of the reactants. These different constraints on the reaction fluxes are shown to originate from the distinct stoichiometric properties of the two classes of networks.

cond-mat.stat-mech↗

arXiv2026

Quantum thermodynamics of the Caldeira-Leggett model with non-equilibrium Gaussian reservoirs

We introduce a non-equilibrium version of the Caldeira-Leggett model in which a quantum particle is strongly coupled to a set of engineered reservoirs. The reservoirs are composed by collections of squeezed and displaced thermal modes, in contrast to the standard case in which the modes are assumed to be at equilibrium. The model proves to be very versatile. Strongly displaced/squeezed reservoirs can be used to generate an effective time dependence in the system Hamiltonian and can be identified as sources of pure work. In the case of squeezing, the time dependence is stochastic and breaks the fluctuation-dissipation relation, this can be reconciled with the second law of thermodynamics by correctly accounting for the energy used to generate the initial non-equilibrium conditions. To go beyond the average description and compute the full heat statistics, we treat squeezing and displacement as generalized Hamiltonians on a modified Keldysh contour. As an application of this technique, we show the quantum-classical correspondence between the heat statistics in the non-equilibrium Caldeira-Leggett model and the statistics of a classical Langevin particle under the action of squeezed and displaced colored noises. Finally, we discuss thermodynamic symmetries of the heat generating function, proving a fluctuation theorem for the energy balance and showing that the conservation of energy at the trajectory level emerges in the classical limit.

quant-ph↗

arXiv2026

Thermalization in Spatially Extended Open Quantum Systems: Local versus Global Markovian Evolution

We investigate the dynamics of a qubit chain locally coupled to a thermal reservoir, modeled through repeated collisions with particles drawn from a heat bath. Under suitable conditions, the resulting Lindblad equation is thermodynamically consistent -- it drives the system toward thermal equilibrium -- while remaining local at short times. This framework reveals a crossover between the global Lindblad equation derived from the secular approximation in weak-coupling theory and the local dissipative models often employed in the literature, which generally fail to ensure thermodynamic consistency.

quant-ph↗

arXiv2026

Singular Behavior of Observables at Hopf Bifurcations

Hopf bifurcations are a universal route to self-sustained oscillations in driven systems. Despite the absence of any singular stationary state, we show that time-averaged observables generically exhibit singularities at the onset of oscillations. The origin of this behavior is geometric: phase averaging over the emergent periodic attractor eliminates odd powers of the oscillation amplitude, while the squared amplitude varies smoothly with the distance from the bifurcation. Consequently, the excess of any smooth time-averaged observable admits an integer-power expansion; observables remain finite but display discontinuities in finite-order derivatives. This yields an Ehrenfest-like hierarchy of Hopf singularities, in which the first nonanalytic derivative is determined by the lowest-order coupling between the observable and the limit-cycle waveform that survives phase averaging. Generic observables therefore exhibit kink singularities, while symmetry or geometric cancellations can suppress lower-order couplings and shift nonanalyticity to higher derivatives. We demonstrate this mechanism in chemical, electronic, and climate oscillators. Our results identify supercritical Hopf bifurcations as a universal mechanism for nonanalytic observable behavior, where singular features arise without any underlying singular stationary state. They thus provide a generic setting for singular behavior without divergence.

cond-mat.stat-mech↗

arXiv2026

Emergence of Open Chemical Reaction Network Thermodynamics within Closed Systems

We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying closed CRNs? While open CRNs provide the standard framework to describe out-of-equilibrium chemical systems, real systems are finite and ultimately relax to equilibrium, leaving the status of this description conceptually unresolved. Here we show that open-CRN behavior arises as an asymptotic regime of closed CRNs when two minimal and physically transparent conditions are met: a time-scale separation, whereby fast reactions effectively act as exchange mechanisms, and an abundance separation, whereby a subset of species behaves as chemostats with diverging chemical capacity. In this regime, both the stochastic dynamics and the thermodynamic structure \ -- including local detailed balance, entropy production, and free-energy balance \ -- emerge to leading order from the underlying closed CRN. Our results apply to arbitrary stoichiometries. They show that chemostats need not be introduced as external idealizations, but instead arise as emergent thermodynamic structures within closed systems, providing a unified and physically grounded foundation for the nonequilibrium thermodynamics of CRNs.

cond-mat.stat-mech↗

arXiv2026

Quantum instanton approach to metastable collective spins

Collective spin systems -- spin ensembles coupled to a common reservoir and effectively described by a single macrospin -- play an important role in both atomic and solid-state physics. Their intrinsic nonlinearity gives rise to multiple long-lived metastable states that ultimately relax to a unique most probable state. This dominant state can change with a control parameter, leading to first-order phase transitions. We develop a real-time instanton approach based on quantum quasiprobability dynamics that captures the stationary state in the large-spin limit and the asymptotic scaling of relaxation rates. We further show that these features are not accurately described by the previously applied semiclassical Wigner approach due to its neglect of non-Gaussian fluctuations.

quant-ph↗

arXiv2026

Integrated covariances as excess observables weighted by currents and activities

Near equilibrium, the symmetric part of the time-integrated steady-state covariance, i.e., the time integral of correlation functions, is governed by the fluctuation-dissipation theorem, while the antisymmetric part vanishes due to Onsager reciprocity. Far from equilibrium, where these principles no longer apply, we develop a unified formalism for both symmetric and antisymmetric components of integrated covariances. We derive exact, computationally tractable expressions for these quantities, valid in arbitrary nonequilibrium steady states of Markov jump processes and Fokker--Planck equation. Both components are expressed in terms of excess observables, a notion central to both statistical physics and reinforcement learning. Furthermore, we establish thermodynamic upper bounds for antisymmetric covariances in terms of (pseudo-)entropy production and cycle affinities. Finally, we show that the speed up of self-averaging induced by nonequilibrium drivings which preserve kinetics (activity) is bounded by the cycle affinities (thermodynamic forces).

cond-mat.stat-mech↗

arXiv2026

Synchronization of thermodynamically consistent stochastic phase oscillators

We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of synchronization. Despite its simplicity, we postulate its relevance for understanding more complex and realistic oscillator systems. In the thermodynamic limit, the model exhibits a continuous nonequilibrium phase transition between the unsynchronized and synchronized states. We show that this transition is not governed by any extremum dissipation principle -- depending on system parameters, synchronization may either reduce or enhance the dissipation. Close to the phase transition, we observe a divergent behavior of fluctuations and responses with $N$ and characterize their universal scaling behavior. In particular, the covariances of the oscillator phases and the local entropy productions are shown to diverge towards $-\infty$, a phenomenon that has not been reported before. Finally, we study the behavior of information-theoretic quantities, demonstrating that mutual information and information flow between oscillators display different scaling with $N$ in synchronized and unsynchronized states, and thus can act as order parameters of synchronization.

cond-mat.stat-mech↗

arXiv2026

Classification of instabilities for the nonideal Brusselator model

We investigate a nonideal, thermodynamically consistent Brusselator reaction-diffusion (RD) system that explicitly incorporates molecular interactions among species in both the diffusion process and the underlying chemical reaction network. Within this framework, we systematically revisit the Cross-Hohenberg classification of instabilities to assess the feasibility and characteristics of the various types of instability arising from the interplay between entropic and energetic contributions. Our analysis demonstrates that only type I and type III instabilities (the Cross-Hohenberg classification) can occur in this system; Energetic contributions do not explicitly generate instabilities, but may implicitly control their occurrence through their influence on the fixed-point (steady-state) concentrations. In cases where instabilities of different types coexist, we show that the resulting patterns are highly sensitive to the relative strengths of the competing instabilities.

cond-mat.stat-mech↗

arXiv2026

Nonequilibrium fluctuation-response relations for state observables

Time-integrated state observables, which quantify the fraction of time spent by the system in a specific pool of states, are important in many fields, such as chemical sensing or the theory of fluorescence spectroscopy. We derive exact identities, called Fluctuation-Response Relations (FRRs), that connect the fluctuations of such observables to their response to external perturbations in nonequilibrium steady state of Markov jump processes. Using these results, we derive a first known upper bound on fluctuations of state observables, as well as some new lower bounds. We further demonstrate how our identities provide a deeper understanding of the mechanistic origin of fluctuations and reveal their properties dependent only on system topology, which may be relevant for model inference using measured data.

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