arXiv subjects

Christian Maes

Publications and source records attributed to Christian Maes.

At least 37 records · Page 2Linked to original sources

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↗

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

Heat capacity of periodically driven two-level systems

We define the heat capacity for steady periodically driven systems and as an example we compute it for dissipative two-level systems where the energy gap is time-modulated. There, as a function of ambient temperature, the Schottky peak remains the dominant feature. Yet, in contrast with equilibrium, the quasistatic thermal response of a nonequilibrium system also reveals kinetic information present in the transition rates; e.g., the heat capacity depends on the time-symmetric reactivities and changes by the presence of a kinetic barrier. It still vanishes though at absolute zero, in accord with an extended Nernst heat postulate, but at a different rate from the equilibrium case. More generally, we discuss the dependence on driving frequency and amplitude.

cond-mat.stat-mech↗

arXiv2024

Acceleration from a clustering environment

We study the effects of correlations in a random environment on a random walker. The dependence of its asymptotic speed on the correlations is a nonperturbative effect as it is not captured by a homogeneous version of the same environment. For a slowly cooling environment, the buildup of correlations modifies the walker's speed and, by so, realizes acceleration. We remark on the possible relevance in the discussion of cosmic acceleration as traditionally started from the Friedmann equations, which, from a statistical mechanical point of view, would amount to a mean-field approximation. Our environment is much simpler though, with transition rates sampled from the one-dimensional Ising model and allowing exact results and detailed velocity characteristics.

cond-mat.stat-mech↗

arXiv2024

Frenetic steering: nonequilibrium-enabled navigation

We explain the steering of slow degrees of freedom by coupling them to driven components for which the time-symmetric reactivities are manipulated. We present the strategy and main principle that make that sort of navigation feasible. For illustration, nonlinear limit cycles (as in the van der Pol oscillator) and strange attractors (as in the Lorenz dynamics) are seen to emerge when the driving in the nonequilibrium medium is kept fixed while the frenesy is tuned to produce the required forces. We imagine that such frenetic steering is available in Life as well, allowing selection of the appropriate biological functioning.

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

Zig-zag dynamics in a Stern-Gerlach spin measurement

The one-century-old Stern-Gerlach setup is paradigmatic for a quantum measurement. We visualize the electron trajectories following the Bohmian zig-zag dynamics. This dynamics was developed in order to deal with the fundamentally massless nature of particles (with mass emerging from the Brout-Englert-Higgs mechanism). The corresponding trajectories exhibit a stochastic zig-zagging, as the result of the coupling between left- and right-handed chiral Weyl states. This zig-zagging persists in the nonrelativistic limit, which will be considered here, and which is described by the Pauli equation for a nonuniform external magnetic field. Our results clarify the different meanings of ``spin'' as a property of the wave function and as a random variable in the Stern-Gerlach setup, and they illustrate the notion of effective collapse. We also examine the case of an EPR-pair. By letting one of the entangled particles pass through a Stern-Gerlach device, the nonlocal influence (action-at-a-distance) on the other particle is manifest in its trajectory, e.g. by initiating its zig-zagging.

quant-ph↗

arXiv2024

Phase diagram and specific heat of a nonequilibrium Curie-Weiss model

Adding activity or driving to a thermal system may modify its phase diagram and response functions. We study that effect for a Curie-Weiss model where the thermal bath switches rapidly between two temperatures. The critical temperature moves with the nonequilibrium driving, opening up a new region of stability for the paramagnetic phase (zero magnetization) at low temperatures. Furthermore, phase coexistence between the paramagnetic and ferromagnetic phases becomes possible at low temperatures. Following the excess heat formalism, we calculate the nonequilibrium thermal response and study its behaviour near phase transitions. Where the specific heat at the critical point makes a finite jump in equilibrium (discontinuity), it diverges once we add the second thermal bath. Finally, (also) the nonequilibrium specific heat goes to zero exponentially fast with vanishing temperature, realizing an extended Third Law.

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

Specific heat of a driven lattice gas

Calorimetry for equilibrium systems aims to determine the available microscopic occupation and distribution of energy levels by measuring thermal response. Nonequilibrium versions are expected to add information on the dynamical accessibility of those states. We perform calculations on a driven exclusion process on an array of particle stations, confirming that expectation. That Markov model produces a fermionic nonequilibrium steady state where the specific heat is computed exactly by evaluating the heat fluxes that are entirely due to a change in ambient temperature. We observe a zero-temperature divergence (violation of the Third Law) when the Fermi energy and the kinetic barrier for loading and emptying become approximately equal. Finally, when the kinetic barrier is density-dependent, a stable low-temperature regime of negative specific heat appears, indicating an anti-correlation between the temperature--dependence of the stationary occupation and the excess heat.

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

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↗

arXiv2023

Calorimetry for active systems

We provide the theoretical basis of calorimetry for a class of active particles subject to thermal noise. Simulating AC-calorimetry, we numerically evaluate the heat capacity of run-and-tumble particles in double-well and in periodic potentials, and of systems with a flashing potential. Low-temperature Schottky-like peaks show the role of activity and indicate shape transitions, while regimes of negative heat capacity appear at higher propulsion speeds. From there, a significant increase in heat capacities of active systems may be inferred at low temperatures, as well as the possibility of diagnostic tools for the activity of self-motile artificial or biomimetic systems based on heat capacity measurements.

cond-mat.stat-mech↗

arXiv2023

Frenetic steering in a nonequilibrium graph

In traditional recognition tasks of neural networks, a potential landscape or cost function guides the system toward patterns using gradient dynamics. That is not how the brain works as its dynamics is far from equilibrium. We present an alternative and proof of principle for pattern recovery in a nonequilibrium model whereby only time-symmetric kinetics are altered. As a mathematical model, a random walker on a randomly-oriented complete graph is subject to finite driving in the direction of the arcs. Some vertices of the graph represent patterns. A first algorithm constructs basins of attraction for these patterns. A second algorithm updates the time-symmetric factors in the transition rates, in order for the walker to quickly reach a pattern and remain there for a sufficiently long time, whenever starting from a vertex in its basin of attraction.

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↗

arXiv2022

Resetting photons

Starting from a frequency diffusion process for a tagged photon which simulates relaxation to the Planck law, we introduce a resetting where photons lower their frequency at random times. We consider two versions, one where the resetting to low frequency is independent of the existing frequency and a second case where the reduction in frequency scales with the original frequency. The result is a nonlinear Markov process where the stationary distribution modifies the Planck law by abundance of low-frequency occupation. The physical relevance of such photon resetting processes can be found in explorations of nonequilibrium effects, e.g., via random expansions of a confined plasma or photon gas or via strongly inelastic scattering with matter.

cond-mat.stat-mech↗