Generalized Fluctuation-Dissipation Theorem for Steady-State Systems

Abstract

The fluctuation-dissipation theorem is a central result of statistical physics, which applies to any system at thermodynamic equilibrium. Its violation is a strong signature of nonequilibrium behavior. We show that for any system with Markovian dynamics, in a nonequilibrium steady state, a proper choice of observables restores a fluctuation-response theorem identical to a suitable version of the equilibrium fluctuation-dissipation theorem. This theorem applies to a broad class of dynamical systems. We illustrate it with linear stochastic dynamics and examples borrowed from the physics of molecular motors and Hopf bifurcations. Finally, we discuss general implications of the theorem.

Generalized Einstein or Green-Kubo Relations for Active Biomolecular Transport

“…This fact imposes a constraint on the ratio between forward and backward rates for any mesoscopic transition that will allow us to express the difference between mobility and dispersion in a physically transparent way. On the technical level, we build on the recent derivation of a general fluctuation-dissipation theorem for NESSs [3][4][5][6]. By directly working in the NESS, our approach is complementary to work that invokes the fluctuation theorem for deriving non-linear response coefficients in higher order expansions around equilibrium [7,8].…”

Entropy production and thermodynamic power of the squeezed thermal reservoir

“…The term˙ = Tr[ˆ ρ S ] defines the effective rate at which entropy is transferred from the surroundings into the system throughout the nonequilibrium potential,ˆ = − lnπ S , originally introduced in a classical context [49,50]. The positivity of˙ is always guaranteed for quantum dynamical semigroups [44], while the emerging second-law inequality in Eq.…”

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

“…The nonequilibrium temperature can have unusual properties. It can depend on which species are observed [15] or change with the steady state [9]. In our Markovian approach, the discreteness and the switching terms have contrasting behavior with respect to changes of the steady state and of J .…”

“…J is a measure of network rigidity and allows one to compute the sensitivity of the steady state to external forces (changes of the parameters μ) [5]. However, (7) contains also the diffusion matrix σ 2 , sometimes interpreted as nonequilibrium "temperature" [9,15]. The nonequilibrium temperature can have unusual properties.…”

“…In nonequilibrium thermodynamics, fluctuation theories are generally obtained from stochastic equations of motion [9]. The dynamics of gene networks can be described by Markov jump processes [10].…”