Driving-induced stability with long-range effects

We give a sufficient condition under which an applied rotation on medium particles stabilizes a slow probe in the rotation center. The symmetric part of the stiffness matrix thus gets a positive Lamb shift with respect to equilibrium. For illustration we take diffusive medium particles with a self-potential in the shape of a Mexican hat, high around the origin. There is a short-range attraction between the medium particles and the heavier probe, all immersed in an equilibrium thermal bath. For no or small rotation force on the medium particles, the origin is an unstable fixed point for the probe and the precise shape of the self-potential at large distances from the origin is irrelevant for the statistical force there. Above a certain rotation threshold, while the medium particles are still repelled from the origin, the probe stabilizes there and more details of the medium-density at large distance start to matter. The effect is robust around the quasi-static limit with rotation threshold only weakly depending on the temperature but the stabilization gets stronger at lower temperatures.Comment: 6 pages, 4 figure

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

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

Calorimetry for active systems

(Thermal) active systems are in physical contact with (at least) two reservoirs: one which is often chemical or radiative and source of low entropy, and one which can be identified with a thermal bath or environment in which energy gets dissipated. Perturbing the temperature, the heat capacity measures the excess heat in addition to the steady ever-existing dissipation. Simulating AC-calorimetry, we numerically evaluate the heat capacity for run-and-tumble particles in double-well and periodic potentials. 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.Comment: 16 pages, 6 figure

Incoherent boundary conditions and metastates

In this contribution we discuss the role which incoherent boundary conditions can play in the study of phase transitions. This is a question of particular relevance for the analysis of disordered systems, and in particular of spin glasses. For the moment our mathematical results only apply to ferromagnetic models which have an exact symmetry between low-temperature phases. We give a survey of these results and discuss possibilities to extend them to some situations where many pure states can coexist. An idea of the proofs as well as the reformulation of our results in the language of Newman-Stein metastates are also presented.Comment: Published at http://dx.doi.org/10.1214/074921706000000176 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

General no-go condition for stochastic pumping

The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemo-mechanical molecular configurations. Pumping refers to generating a net current, e.g. per period in the time-dependence, through a cycle of consecutive states. The working of artificial machines or synthesized molecular motors depends on it. In this paper we give short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit. It allows to exclude certain protocols in the working of chemical motors where only the depth of the energy well is changed in time and not the barrier height between pairs of states. We also show how pre-existing steady state currents are in general modified with a multiplicative factor when this time-dependence is turned on.Comment: 8 pages; v2: minor changes, 1 reference adde