Nonequilibrium temperature response for stochastic overdamped systems

The thermal response of nonequilibrium systems requires the knowledge of concepts that go beyond entropy production. This is showed for systems obeying overdamped Langevin dynamics, either in steady states or going through a relaxation process. Namely, we derive the linear response to perturbations of the noise intensity, mapping it onto the quadratic response to a constant small force. The latter, displaying divergent terms, is explicitly regularized with a novel path-integral method. The nonequilibrium equivalents of heat capacity and thermal expansion coefficient are two applications of this approach, as we show with numerical examples.Comment: 23 pages, 2 figure

Inflow rate, a time-symmetric observable obeying fluctuation relations

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find detailed and integral fluctuation relations for the (time integrated) difference between "entrance rate" and escape rate in mesoscopic jump systems. Such "inflow rate", which is even under time reversal, represents the discrete-state equivalent of the phase space contraction rate. Indeed, it becomes minus the divergence of forces in the continuum limit to overdamped diffusion. This establishes a formal connection between reversible deterministic systems and irreversible stochastic ones, confirming that fluctuation theorems are largely independent of the details of the underling dynamics.Comment: v3: published version, slightly shorter title and abstrac

Non-isothermal fluctuating hydrodynamics and Brownian motion

The classical theory of Brownian dynamics follows from coarse-graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally non-isothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the non-isothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.Comment: 9 page

About the role of chaos and coarse graining in Statistical Mechanics

We discuss the role of ergodicity and chaos for the validity of statistical laws. In particular we explore the basic aspects of chaotic systems (with emphasis on the finite-resolution) on systems composed of a huge number of particles.Comment: Summer school `Fundamental Problems in Statistical Physics' (Leuven, Belgium), June 16-29, 2013. To be published in Physica

Negative differential response in chemical reactions

Reaction currents in chemical networks usually increase when increasing their driving affinities. But far from equilibrium the opposite can also happen. We find that such negative differential response (NDR) occurs in reaction schemes of major biological relevance, namely, substrate inhibition and autocatalysis. We do so by deriving the full counting statistics of two minimal representative models using large deviation methods. We argue that NDR implies the existence of optimal affinities that maximize the robustness against environmental and intrinsic noise at intermediate values of dissipation. An analogous behavior is found in dissipative self-assembly, for which we identify the optimal working conditions set by NDR.Comment: Main text and S

Thermal response of nonequilibrium RC-circuits

We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response theory for nonequilibrium overdamped stochastic systems. To validate these results, we introduce a reweighting procedure that mimics the actual realization of the perturbation and allows extracting the susceptibility of the system from steady state data. This procedure is closely related to other fluctuation-response relations based on the knowledge of the steady state probability distribution. As an example, we show that the nonequilibrium heat capacity in general does not correspond to the correlation between the energy of the system and the heat flowing into it. Rather, also non-dissipative aspects are relevant in the nonequilbrium fluctuation response relations.Comment: 2 figure

Four out-of-equilibrium lectures

A collection of published papers on the subject of classical nonequilibrium statistical mechanics. Mainly stochastic systems are considered, with special regard to applications in soft matter physic

Mesoscopic virial equation for nonequilibrium statistical mechanics

We derive a class of mesoscopic virial equations governing energy partition between conjugate position and momentum variables of individual degrees of freedom. They are shown to apply to a wide range of nonequilibrium steady states with stochastic (Langevin) and deterministic (Nos\'e--Hoover) dynamics, and to extend to collective modes for models of heat-conducting lattices. A generalised macroscopic virial theorem ensues upon summation over all degrees of freedom. This theorem allows for the derivation of nonequilibrium state equations that involve dissipative heat flows on the same footing with state variables, as exemplified for inertial Brownian motion with solid friction and overdamped active Brownian particles subject to inhomogeneous pressure.Comment: 14 pages, 3 figures. Some revision