arXiv subjects

Christian Maes

Publications and source records attributed to Christian Maes.

At least 19 recordsLinked to original sources

arXiv2026

Entropy and Frenesy: the arrow and the bustle of time

Nonequilibrium statistical mechanics is the science of time as it manifests itself in the transient or steady entropy producing dynamical condition of many-body systems. Beyond the vivid multiformity of the phenomena themselves, three foundational issues lie at its heart. The first question concerns the very origin of entropy production, which gives macroscopic processes their direction and thereby defines the arrow of time: how does an atomistic mechanical world give rise to dissipated heat, thermalization, and time-reversal symmetry breaking? The second asks why, far beyond the familiar behavior of equilibrium systems, driving or agitation may produce and select stable and functionally rich structures: what is it about far-from-equilibrium, low-entropy driving that unleashes the wealth and intricacy of the natural world? The third issue is partly methodological: to determine how, and for which subclass of such wildly diverse nonequilibrium systems, a systematic, unified description and modeling from first principles remains possible. This essay addresses these issues in an informal, semi-popular-science style, offering a personally engaging yet wide-ranging introduction to the complementary roles of entropy production and the less familiar, more recently coined notion of frenesy in the dynamical fluctuations of steadily driven systems. Together, we argue, they provide a more complete starting point for understanding physical time on mesoscopic to macroscopic scales.

physics.pop-ph↗

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 $\beta_c$ as the magnetic susceptibility. The new Curie temperature decreases with the driving, and we find critical exponent $\alpha=1$ for $\beta\downarrow \beta_c$, and $\alpha\simeq 0.86$ for $\beta\uparrow \beta_c$, 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

An agitated oscillator chain

We study how the stationary dynamics of an oscillator chain is modified when coupled to a bath of run-and-tumble particles. First, assuming time-scale separation, we derive the induced Langevin chain dynamics with explicit expressions for the streaming term, friction coefficient, and noise amplitude. At high persistence of the run-and-tumble particle bath, the linear friction turns negative, creating an instability. Second, we find that this anti-damping is arrested at long times due to nonlinear effects, reminiscent of a Rayleigh oscillator. We conclude that a passive harmonic chain can be transformed by its coupling to active matter into a self-sustained fluctuating medium with many-body Rayleigh-like dynamics. That transfer of activity results in pulsations of the displacements, spatial oscillations, and the emergence of persistence in velocities along the chain.

cond-mat.stat-mech↗

arXiv2026

A Rayleigh criterion for mechanical instability: inducing activity by chemo-mechanical coupling

Instabilities in thermodynamic systems are often undesirable, as they can lead to loss of control or even catastrophic behavior. Yet, the same mechanisms can also generate rich nonequilibrium behavior and may play a constructive role in living systems. We introduce a theoretical framework, inspired by Rayleigh's analysis of thermoacoustic instabilities, to study the emergence of mechanical activity. In particular, we derive Rayleigh-like criteria governing the onset of activity and the generation of rotational motion in a slow Newtonian probe coupled to driven chemical processes, described by Markov jump processes. These criteria are expressed in terms of the phase relation between entropic and frenetic contributions, providing a transparent condition for when chemical driving results in sustained rotational or active mechanical motion.

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

Negative Differential Heat Conductivity in a Harmonic Chain Coupled to a Particle Reservoir

When coupling thermal baths at different temperatures, negative differential thermal conductivity is typically attributed to nonlinear interactions in the connecting medium. In this work, we demonstrate that such an effect can arise purely from the nature of the thermal baths and their coupling with the medium. Specifically, we construct a bath composed of overdamped thermal particles, which is coupled to one end of a harmonic chain, while the other end is connected to a standard Langevin heat bath. By analyzing the steady-state heat current, we observe significant negative differential thermal conductivity. In particular, as the temperature difference between the two baths diverges, the steady-state heat current through the chain vanishes. The effect is thermokinetic: we compute the effective dissipative coefficient and we find that it scales inversely with the square of the temperature of the particle bath in the high-temperature limit, resulting in an asymptotic decoupling between the bath and the chain. Our results highlight that nonequilibrium transport properties can be strongly influenced by the structure of the environment and its coupling to the system, even in otherwise linear systems.

cond-mat.stat-mech↗

arXiv2026

Relaxation to nonequilibrium

We describe the structure of relaxation for a steadily driven macroscopic body. The time-evolution is characterized as the zero-cost flow for a nonequilibrium and nonlinear extension of the Onsager-Machlup action governing the dynamical fluctuations. The approach hinges on two main elements: the principle of local detailed balance, which identifies the relevant thermodynamic forces, and the canonical decomposition of the frenesy into a Legendre pair. Notably, it is the time-symmetric component of the Lagrangian, the frenesy, that shapes the structure of the macroscopic evolution for given forcing. We add a simple argument for why the nonequilibrium entropy, which governs the static macroscopic fluctuations of the system, is monotone in time. The results can be interpreted as the steady nonequilibrium extension of GENERIC where relaxation to equilibrium is governed by a dissipative gradient flow superimposed on a Hamiltonian flow.

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↗

arXiv2026

What is nonequilibrium?

Lecture notes on elements of nonequilibrium statistical mechanics: (1) a characterization of the nonequilibrium condition, largely by contrast to equilibrium; (2) a retelling of some of the great performances of the more distant past, including the perspectives of Boltzmann and Onsager; and (3) more recent methods and concepts, from local detailed balance and the identification of entropy fluxes to dynamical fluctuation theory, and the importance of dynamical activity.

cond-mat.stat-mech↗

arXiv2025

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↗

arXiv2025

Coupling an elastic string to an active bath: the emergence of inverse damping

We consider a slow elastic string with Klein-Gordon dynamics coupled to a bath of run-and-tumble particles. We derive and solve the induced Langevin-Klein-Gordon string dynamics with explicit expressions for the streaming term, friction coefficient, and noise variance. These parameters are computed exactly in a weak coupling expansion. The induced friction is a sum of two terms: one entropic, proportional to the noise variance as in the Einstein relation for a thermal equilibrium bath, and a frenetic contribution that can take both signs. The frenetic part wins for higher bath persistence, making the total friction negative, and hence creating a wave instability akin to inverse Landau damping. However, this acceleration decreases and eventually disappears when the propulsion speed of the active particles becomes much higher. Detailed simulations confirm the initial growth driven by this anti-damping.

cond-mat.stat-mech↗

arXiv2025

Transfer of active motion from medium to probe via the induced friction and noise

Can activity be transmitted from smaller to larger scales? We report on such a transfer from a homogeneous active medium to a Newtonian spherical probe. The active medium consists of faster and dilute self-propelled particles, modeled as run-and-tumble particles in 1D or as active Brownian particles in 2D. We derive the reduced fluctuating dynamics of the probe, valid for arbitrary probe velocity, characterized by velocity-dependent friction and noise. In addition to a standard passive regime, we identify peculiar active regimes where the probe becomes self-propelled with high persistence, and its velocity distribution begets peaks at nonzero values. These features are quantitatively confirmed by numerical simulations of the joint probe-medium system. The emergence of active regimes depends not only on the far-from-equilibrium nature of the medium but also on the probe-medium coupling. Our findings reveal how, solely via the induced friction and noise, persistence can cross different scales to transfer active motion.

cond-mat.stat-mech↗

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

Specific heat of the driven Curie-Weiss model

Applying a time-periodic magnetic field to the standard ferromagnetic Curie-Weiss model brings the spin system in a steady out-of-equilibrium condition. We recall how the hysteresis gets influenced by the amplitude and the frequency of that field, and how an amplitude- and frequency-dependent (dynamical) critical temperature can be discerned. The dissipated power measures the area of the hysteresis loop and changes with temperature. The excess heat determines a nonequilibrium specific heat giving the quasistatic response. We compute that specific heat, which appears to diverge at the critical temperature, quite different from the equilibrium case.

cond-mat.stat-mech↗

arXiv2024

Noether's theorem applied to GENERIC

The last decades have seen growing interest in connecting principles of thermodynamics with methods from analytical mechanics. The thermodynamic formalism has become an inspiring framework in the study of smooth dynamical systems, and pioneering works of Helmholtz, Clausius, and Boltzmann have been reinstated as possible dynamical foundations of the (first part of the) Heat Theorem. The present paper follows the work of Wald et al., where black hole entropy was identified as a Noether charge. The adiabatic invariance of the thermodynamic entropy indeed invites a connection with Noether's theorem, and has been the subject of various papers. Here we add the case of GENERIC, a macroscopic dynamics whose acronym stands for ``General Equation for Non-Equilibrium Reversible-Irreversible Coupling''. Its evolution has two contributions: a dissipative part, which is of a generalized gradient descent form, and a Hamiltonian flow. We consider a quasistatic protocol for external parameters, and we embed GENERIC as the zero-cost flow for a Lagrangian governing the dynamical fluctuations. We find a continuous symmetry of the corresponding path-space action with the thermodynamic entropy as Noether charge, both in the Lagrangian and Hamiltonian formalisms. We make the calculations explicit through the example of an inertial probe with nonlinear friction.

cond-mat.stat-mech↗

arXiv2024

First part of Clausius heat theorem in terms of Noether's theorem

After Helmholtz, the mechanical foundation of thermodynamics included the First Law $d E = \delta Q + \delta W$, and the first part of the Clausius heat theorem $\delta Q^\text{rev}/T = dS$. The resulting invariance of the entropy $S$ for quasistatic changes in thermally isolated systems invites a connection with Noether's theorem (only established later). In this quest, we continue an idea, first brought up by Wald in black hole thermodynamics and by Sasa $\textit{et al.}$ in various contexts. We follow both Lagrangian and Hamiltonian frameworks, and emphasize the role of Killing equations for deriving a First Law for thermodynamically consistent trajectories, to end up with an expression of ``heat over temperature'' as an exact differential of a Noether charge.

cond-mat.stat-mech↗

arXiv2024

The induced friction on a probe moving in a nonequilibrium medium

Using a powerful combination of projection-operator method and path-space response theory, we derive the fluctuation dynamics of a slow inertial probe coupled to a steady nonequilibrium medium under the assumption of time-scale separation. The nonequilibrium is realized by external nongradient driving on the medium particles or by their (athermal) active self-propulsion. The resulting friction on the probe is an explicit time-correlation for medium observables and is decomposed into two terms, one entropic, proportional to the noise variance as in the Einstein relation for equilibrium media, and a frenetic term that can take both signs. As an illustration, we give the exact expressions for the linear friction coefficient and noise amplitude of a probe in a rotating run-and-tumble medium. We find a transition to absolute negative probe friction as the nonequilibrium medium exhibits sufficient and persistent rotational current. There, the run-away of the probe to high speeds realizes a nonequilibrium-induced acceleration. Simulations show that its speed finally saturates, yielding a symmetric stationary probe-momentum distribution with two peaks.

cond-mat.stat-mech↗