arXiv subjects

Faezeh Khodabandehlou

Publications and source records attributed to Faezeh Khodabandehlou.

17 recordsLinked to original sources

arXiv2026

Local Detailed Balance in the Lorenz Model: Replaces the Butterfly with Frenetic Bursting

The Lorenz system is the canonical low-order model of convective instability, yet its dissipative and driving terms have never been checked against, nor constructed from, an explicit thermodynamic bookkeeping. We derive a modification that satisfies the local-detailed-balance condition for macroscopic relaxation toward nonequilibrium steady states, thereby identifying the thermodynamic force, entropy-production rate and frenesy of the resulting flow. The resulting model produces a transition from a quiescent fixed point to a robust, large-amplitude relaxation oscillation, closely analogous to recharge-discharge oscillator paradigms used for the El Nino-Southern Oscillation. The system alternates between a long, nearly reversible recharge phase and a brief, violently frenetic discharge burst, during which essentially all of the cycle's activity and entropy production is concentrated.

cond-mat.stat-mech↗

arXiv2026

Critical behavior of the driven Curie-Weiss model

We complete the phase diagram of the macroscopic Curie-Weiss magnet in a time-periodic external field, as a function of temperature and driving parameters. There is a regime (large enough driving amplitude and frequency, at low temperatures) where stable paramagnetic and ferromagnetic phases coexist. In particular, we present a new detailed analysis of the (nonequilibrium) specific heat, diverging at the same critical inverse temperature $β_c$ as the magnetic susceptibility. The new Curie temperature decreases with the driving, and we find critical exponent $α=1$ for $β\downarrow β_c$, and $α\simeq 0.86$ for $β\uparrow β_c$, even for small driving. A Floquet analysis shows the nature of the criticality, which is dynamical, with implications that remain unseen and are mostly impossible when the system is in thermal equilibrium.

cond-mat.stat-mech↗

arXiv2026

Specific heat of thermally driven chains

We investigate the thermal responses of a harmonic oscillator chain coupled at its boundaries to heat baths held at different temperatures. This setup sustains a steady energy flux, continuously dissipating heat into both reservoirs. By introducing slow variations in the bath temperatures, we quantify the resulting excess heat currents and thereby obtain the nonequilibrium heat capacity matrix at fixed but arbitrary temperature differences. We demonstrate the existence of a well-defined thermodynamic limit for long chains. The specific heat associated with energy exchanges with a single bath depends on the difference in friction coefficients governing the system-bath couplings. That thermokinetic effect is typical for nonequilibrium response. When the couplings with the thermal baths acquire temperature dependence, the specific heat correspondingly inherits a nontrivial temperature dependence, in sharp contrast with equilibrium. Our results provide the first explicit determination of specific heat(s) in a locally interacting, spatially extended driven system. Beyond its exact solvability, the model may offer a natural nonequilibrium extension of the Dulong-Petit law, capturing the high-temperature behavior of driven molecules.

cond-mat.stat-mech↗

arXiv2026

Quasistatic response for nonequilibrium processes: evaluating the Berry potential and curvature

We investigate how introducing slow, time-dependent perturbations to a steady, nonequilibrium process alters the expected (excess) values of important observables, such as the dynamical activity and entropy flux. When we make a cyclic thermodynamic transformation, the excesses are described in terms of a (geometric) Berry phase with corresponding Berry potential and Berry curvature quantifying the response. Focussing on Markov jump processes, we show how a non-zero Berry curvature leads to a breakdown of the thermodynamic Maxwell relations and of the Clausius heat theorem. We also present a variant of the Aharonov-Bohm effect in which the parameters follow a curve with vanishing Berry curvature, but the system still experiences a nonzero Berry phase. Finally, we identify (sufficient) no-localization conditions in terms of mean first-passage times under which the corresponding Berry potentials and curvatures vanish at absolute zero, extending, for arbitrary driving, e.g., the case of vanishing heat capacity as for the Nernst postulate.

cond-mat.stat-mech↗

arXiv2026

Bringing calorimetry (back) to life

Micro-calorimetry offers significant potential as a quantitative method for studying the structure and function of biological systems, for instance, by probing the excess heat released by cellular or sub-cellular structures, isothermal or not, when external parameters change. We present the conceptual framework of nonequilibrium calorimetry, and as illustrations, we compute the heat capacity of biophysical models with few degrees of freedom related to ciliar motion (rowing model) and molecular motor motion (flashing ratchets). Our quantitative predictions reveal intriguing dependencies of the (nonequilibrium) heat capacity as a function of relevant biophysical parameters, which can even take negative values as a result of biological activity.

physics.bio-ph↗

arXiv2025

Negative specific heats: where Clausius and Boltzmann entropies separate

Steady nonequilibria dissipate energy and, when changing external parameters, an extra or excess heat accompanies the relaxation to the new nonequilibrium condition. For nonequilibrium systems in contact with a thermal bath, the heat capacity is defined as that excess heat per degree temperature for a quasistatic change of the bath temperature. It is fairly common to find negative heat capacities for steady nonequilibrium systems, in contrast with the situation for systems in thermal equilibrium. We discuss and illustrate the origin of that negative thermal response using Markov models. We find that the negativity results from an anticorrelation between quasipotential and (a change in) pseudopotential, the first measuring (excess) heat (and Clausius entropy), and the latter being related to the Boltzmann entropy. It can be quantified via an appropriate choice of effective temperatures.

cond-mat.stat-mech↗

arXiv2024

Affine relationships between steady currents

Perturbing transition rates in a steady nonequilibrium system, e.g. modelled by a Markov jump process, causes a change in the local currents. Their susceptibility is usually expressed via Green-Kubo relations or their nonequilibrium extensions. However, we may also wish to directly express the mutual relation between currents. Such a nonperturbative interrelation was discovered by P.E. Harunari et al. in [1] by applying algebraic graph theory showing the mutual linearity of currents over different edges in a graph. We give a novel and shorter derivation of that current relationship where we express the current-current susceptibility as a difference in mean first-passage times. It allows an extension to multiple currents, which remains affine but the relation is not additive.

cond-mat.stat-mech↗

arXiv2024

Close-to-equilibrium heat capacity

Close to equilibrium, the excess heat governs the static fluctuations. We study the heat capacity in that McLennan regime, i.e., in linear order around equilibrium, using an expression in terms of the average energy that extends the equilibrium formula in the canonical ensemble. It is derivable from an entropy and it always vanishes at zero temperature. Any violation of an extended Third Law is, therefore, a nonlinear effect.

cond-mat.stat-mech↗

arXiv2024

Nonequilibrium Third Law of Thermodynamics

The extended Third Law of thermodynamics for nonequilibrium jump processes is studied in previous collaborative papers (Kh et al.,2023) [1,2], where the nonequilibrium heat capacity and the excess heat with the corresponding quasipotential are introduced. The extended Third Law states that the nonequilibrium heat capacity vanishes under two conditions as the temperature approaches zero. The current paper presents a concise overview of key papers addressing the nonequilibrium calorimetry and the nonequilibrium Nernst postulate (the nonequilibrium Third Law of thermodynamics). The quasipotential is a crucial quantity to calculate the nonequilibrium heat capacity. The new result presented in this work includes an interpretation of the quasipotential in terms of the mean time taken by the Markov jump process, starting from a given state, to reach other states for the first time.

cond-mat.stat-mech↗

arXiv2024

The Sun within: active processes from two-temperature models

We propose an embedding of standard active particle models in terms of two-temperature processes. One temperature refers to an ambient thermal bath, and the other temperature effectively describes ``hot spots,'' i.e., systems with few degrees of freedom showing important population homogenization or even inversion of energy levels as a result of activation. As a result, the effective Carnot efficiency would get much higher than for our standard macroscopic thermal engines, making connection with the recent conundrum of hot mitochondria. Moreover, that setup allows to quantitatively specify the resulting nonequilibrium driving, useful in particular for bringing the notion of heat into play, and making easy contact with thermodynamic features. Finally, we observe that the shape transition in the steady low-temperature behavior of run-and-tumble particles (with the interesting emergence of edge states at high persistence) is stable and occurs for all temperature differences, including close-to-equilibrium.

cond-mat.stat-mech↗

arXiv2024

Local detailed balance for active particle models

Starting from a Huxley-type model for an agitated vibrational mode, we propose an embedding of standard active particle models in terms of two-temperature processes. One temperature refers to an ambient thermal bath, and the other temperature effectively describes ``hot spots,'' i.e., systems with few degrees of freedom showing important population homogenization or even inversion of energy levels as a result of activation. That setup admits to quantitatively specifying the resulting nonequilibrium driving, rendering local detailed balance to active particle models, and making easy contact with thermodynamic features. In addition, we observe that the shape transition in the steady low-temperature behaviour of run-and-tumble particles (with the interesting emergence of edge states at high persistence) is stable and occurs for all temperature differences, including close to equilibrium.

cond-mat.stat-mech↗

arXiv2023

On the Poisson equation for nonreversible Markov jump processes

We study the solution $V$ of the Poisson equation $LV + f=0$ where $L$ is the backward generator of an irreducible (finite) Markov jump process and $f$ is a given centered state function. Bounds on $V$ are obtained using a graphical representation derived from the Matrix Forest Theorem and using a relation with mean first-passage times. Applications include estimating time-accumulated differences during relaxation toward a steady nonequilibrium regime.

math.PR↗

arXiv2023

Drazin-Inverse and heat capacity for driven random walks on the ring

We apply single and double tree-like representations of Markov jump processes on $\mathbb{Z}_N$ for obtaining their nonequilibrium heat capacity and for taking the diffusion limit $N\uparrow \infty$. The main tool is a graphical representation of the Drazin-inverse of the backward generator. In that way, the combination of algebraic and graph-theoretical approaches enables an exact computation of an important nonequilibrium quantity (excess heat) for Markov jump processes.

math.PR↗

arXiv2023

A Nernst heat theorem for nonequilibrium jump processes

We discuss via general arguments and examples when and why the steady nonequilibrium heat capacity vanishes with temperature. The framework is the one of Markov jump processes on finite connected graphs where the condition of local detailed balance allows to identify the heat fluxes, and where the discreteness more easily enables sufficient nondegeneracy of the stationary distribution at absolute zero, as under equilibrium. However, for the nonequilibrium extension of the Third Law, a dynamic condition is needed as well: the low-temperature dynamical activity and accessibility of the dominant state must remain sufficiently high so that relaxation times do not start to dramatically differ between different initial states. It suffices in fact that the relaxation times do not exceed the dissipation time.

cond-mat.stat-mech↗

arXiv2023

The vanishing of excess heat for nonequilibrium processes reaching zero ambient temperature

We present the mathematical ingredients for an extension of the Third Law of Thermodynamics (Nernst heat postulate) to nonequilibrium processes. The central quantity is the excess heat which measures the quasistatic addition to the steady dissipative power when a parameter in the dynamics is changed slowly. We prove for a class of driven Markov jump processes that it vanishes at zero environment temperature. Furthermore, the nonequilibrium heat capacity goes to zero with temperature as well. Main ingredients in the proof are the matrix-forest theorem for the relaxation behavior of the heat flux, and the matrix-tree theorem giving the low-temperature asymptotics of the stationary probability. The main new condition for the extended Third Law requires the absence of major (low-temperature induced) delays in the relaxation to the steady dissipative structure.

cond-mat.stat-mech↗

arXiv2022

Exact computation of heat capacities for active particles on a graph

The notion of a nonequilibrium heat capacity is important for bio-energetics and for calorimetry of active materials more generally. It centers around the notion of excess heat or excess work dissipated during a quasistatic relaxation between different nonequilibrium conditions. We give exact results for active random walks moving in an energy landscape on a graph, based on calculations employing the matrix-tree and matrix-forest theorems. That graphical method applies to any Markov jump process under the physical condition of local detailed balance, and is not restricted to the examples given in this paper.

cond-mat.stat-mech↗

arXiv2022

Trees and forests for nonequilibrium purposes: an introduction to graphical representations

Using local detailed balance we rewrite the Kirchhoff formula for stationary distribution of Markov jump processes in terms of a physically interpretable tree-ensemble. We use that arborification of path-space integration to derive a McLennan-tree characterization close to equilibrium, as well as to obtain response formula for the stationary distribution in the asymptotic regime of large driving. Graphical expressions of currents and of traffic are obtained, allowing the study of various asymptotic regimes. Finally, we present how the matrix-forest theorem gives a representation of quasi-potentials, as used e.g. for computing excess work and heat in nonequilibrium thermal physics. A variety of examples illustrate and explain the graph elements and constructions.

cond-mat.stat-mech↗