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.

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.

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 that 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 of Thermodynamics, 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.

Inducing a bound state between active particles.

We show that two active particles can form a bound state by coupling to a driven nonequilibrium environment. We specifically investigate the case of two mutually noninteracting run-and-tumble probes moving on a ring, each in short-range interaction with driven colloids. Under conditions of timescale separation, these active probes become trapped in bound states.

Fluctuating Motion in an Active Environment.

We derive the fluctuation dynamics of a probe in weak coupling with a living medium, modeled as particles undergoing an active Ornstein-Uhlenbeck dynamics. Nondissipative corrections to the fluctuation-dissipation relation are written out explicitly in terms of time correlations in the active medium. A first term changes the inertial mass of the probe as a consequence of the persistence of the active medium.

Active velocity processes with suprathermal stationary distributions and long-time tails.

When a particle moves through a spatially random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy localization. The result is a unifying framework for the emergence of heavy tails in the velocity distribution, relevant for understanding the power-law decay in the electron velocity distribution of space plasma or more generally for explaining non-Maxwellian behavior of driven gases.

Nonequilibrium corrections to gradient flow.

The force on a probe induced by a nonequilibrium medium is in general nongradient. We detail the mechanism of this feature via nonequilibrium response theory. The emergence of nongradient forces is due to a systematic "twist" of the excess frenesy with respect to the entropy flux, in response to changes in the coupling or in the position of the probe in the nonequilibrium medium.

Active processes in one dimension.

We consider the thermal and athermal overdamped motion of particles in one-dimensional geometries where discrete internal degrees of freedom (spin) are coupled with the translational motion. Adding a driving velocity that depends on the time-dependent spin constitutes the simplest model of active particles (run-and-tumble processes) where the violation of the equipartition principle and of the Sutherland-Einstein relation can be studied in detail even when there is generalized reversibility. We give an example (with four spin values) where the irreversibility of the translational motion manifests itself only in higher-order (than two) time correlations.

Frenetic Bounds on the Entropy Production.

We give a systematic derivation of positive lower bounds for the expected entropy production (EP) rate in classical statistical mechanical systems obeying a dynamical large deviation principle. The logic is the same for the return to thermodynamic equilibrium as it is for steady nonequilibria working under the condition of local detailed balance. We recover there recently studied "uncertainty" relations for the EP, appearing in studies about the effectiveness of mesoscopic machines.

The modified Langevin description for probes in a nonlinear medium.

When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe's effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is no longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath.

Mathematical model suitable for efficient simulation of thin semi-flexible polymers in complex environments.

We present an alternative approach to simulations of semi-flexible polymers. In contrast with the usual bead-rod compromise between bead-spring and rigid rod models, we use deformable cylindrical segments as basic units of the polymer. The length of each segment is not preserved with end points diffusing under constraints keeping the polymer chain nature intact.

How Statistical Forces Depend on the Thermodynamics and Kinetics of Driven Media.

We study the statistical force of a nonequilibrium environment on a quasistatic probe. In the linear regime, the isothermal work on the probe equals the excess work for the medium to relax to its new steady condition with a displaced probe. Also, the relative importance of reaction paths can be measured via statistical forces, and from second order onwards the force on the probe reveals information about nonequilibrium changes in the reactivity of the medium.

Friction and noise for a probe in a nonequilibrium fluid.

We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modeled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium.

Frenetic aspects of second order response.

Starting from the second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called frenetic contribution in the second order around equilibrium is illustrated in different physical examples, such as for non-thermodynamic aspects in the coupling between a system and reservoir, for the dependence on disorder in the dielectric response and for the nonlinear correction to the Sutherland-Einstein relation. More generally, the way in which a system's dynamical activity changes by perturbation is visible (only) from the nonlinear response.

Frenetic origin of negative differential response.

The Green-Kubo formula for linear response coefficients is modified when dealing with nonequilibrium dynamics. In particular, negative differential conductivities are allowed to exist away from equilibrium. We give a unifying framework for such a negative differential response in terms of the frenetic contribution in the nonequilibrium formula.

From Langevin to generalized Langevin equations for the nonequilibrium Rouse model.

We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain.

Monotonic return to steady nonequilibrium.

We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump or diffusion processes it measures an excess in dynamical activity rates.

General no-go condition for stochastic pumping.

The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemomechanical molecular configurations. Pumping refers to generating a net current, e.g.

Fluctuations and response of nonequilibrium states.

A generalized fluctuation-response relation is found for thermal systems driven out of equilibrium. Its derivation is independent of many details of the dynamics, which is only required to be first order. The result gives a correction to the equilibrium fluctuation-dissipation theorem, in terms of the correlation between observable and excess in dynamical activity caused by the perturbation.

Nonequilibrium relation between potential and stationary distribution for driven diffusion.

We investigate the relation between an applied potential and the corresponding stationary-state occupation for nonequilibrium and overdamped diffusion processes. This relation typically becomes long ranged resulting in global changes for the relative density when the potential is locally perturbed, and inversely, we find that the potential needs to be wholly rearranged for the purpose of creating a locally changed density. The direct question, determining the density as a function of the potential, comes under the response theory out of equilibrium.

Symmetries of the ratchet current.

Recent advances in nonequilibrium statistical mechanics shed new light on the ratchet effect. The ratchet motion can thus be understood in terms of symmetry (breaking) considerations. We introduce an additional symmetry operation besides time reversal, that switches between two modes of operation.

Amplification of compressional magnetohydrodynamic waves in systems with forced entropy oscillations.

The propagation of compressional MHD waves is studied for an externally driven system. It is assumed that the combined action of the external sources and sinks of the entropy results in the harmonic oscillation of the entropy (and temperature) in the system. It is found that with the appropriate resonant conditions fast and slow waves get amplified due to the phenomenon of parametric resonance.

Fluctuation symmetries for work and heat.

We consider a particle dragged through a medium at constant temperature as described by a Langevin equation with a time-dependent potential. The time dependence is specified by an external protocol. We give conditions on potential and protocol under which the fluctuations of the dissipative work satisfy an exact symmetry for all times.

Time-symmetric fluctuations in nonequilibrium systems.

For nonequilibrium steady states, we identify observables whose fluctuations satisfy a general symmetry and for which a new reciprocity relation can be shown. Unlike the situation in recently discussed fluctuation theorems, these observables are time-reversal symmetric. That is essential for exploiting the fluctuation symmetry beyond linear response theory.

Enstrophy dissipation in two-dimensional turbulence.

Insight into the problem of two-dimensional turbulence can be obtained by an analogy with a heat conduction network. It allows the identification of an entropy function associated with the enstrophy dissipation and that fluctuates around a positive (mean) value. While the corresponding enstrophy network is highly nonlocal, the direction of the enstrophy current follows from the Second Law of Thermodynamics.