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.

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores.

The system of a driven dense colloid mixture in a tube with diameter comparable to particle size is modeled by a generalization of the asymmetric simple exclusion process (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site and by considering two species of particles, which differ in size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of the Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results.

Separation of dense colloidal suspensions in narrow channels: A stochastic model.

The flow of a colloidal suspension in a narrow channel of periodically varying width is described by the one-dimensional generalized asymmetric exclusion process. Each site admits multiple particle occupancy. We consider particles of two different sizes.

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.

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.

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.

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.

Universal oscillations in counting statistics.

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants n(m) of the number n of passed charges to very high orders (up to m = 15) for electron transport through a quantum dot.