Showing papers by "Vojkan Jaksic published in 2017"

Entropic Fluctuations in Thermally Driven Harmonic Networks

Abstract: We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence and uniqueness of the steady state of the resulting process, we construct a canonical entropy production functional $$S^t$$ which satisfies the Gallavotti–Cohen fluctuation theorem. More precisely, we prove that there exists $$\kappa _c>\frac{1}{2}$$ such that the cumulant generating function of $$S^t$$ has a large-time limit $$e(\alpha )$$ which is finite on a closed interval $$[\frac{1}{2}-\kappa _c,\frac{1}{2}+\kappa _c]$$ , infinite on its complement and satisfies the Gallavotti–Cohen symmetry $$e(1-\alpha )=e(\alpha )$$ for all $$\alpha \in {\mathbb {R}}$$ . Moreover, we show that $$e(\alpha )$$ is essentially smooth, i.e., that $$e'(\alpha )\rightarrow \mp \infty $$ as $$\alpha \rightarrow \tfrac{1}{2}\mp \kappa _c$$ . It follows from the Gartner–Ellis theorem that $$S^t$$ satisfies a global large deviation principle with a rate function I(s) obeying the Gallavotti–Cohen fluctuation relation $$I(-s)-I(s)=s$$ for all $$s\in {\mathbb {R}}$$ . We also consider perturbations of $$S^t$$ by quadratic boundary terms and prove that they satisfy extended fluctuation relations, i.e., a global large deviation principle with a rate function that typically differs from I(s) outside a finite interval. This applies to various physically relevant functionals and, in particular, to the heat dissipation rate of the network. Our approach relies on the properties of the maximal solution of a one-parameter family of algebraic matrix Riccati equations. It turns out that the limiting cumulant generating functions of $$S^t$$ and its perturbations can be computed in terms of spectral data of a Hamiltonian matrix depending on the harmonic potential of the network and the parameters of the Langevin reservoirs. This approach is well adapted to both analytical and numerical investigations.

Fluctuation Theorem and Thermodynamic Formalism

Abstract: We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical systems on compact metric spaces, and extend it to empirical measures, all continuous potentials, and all weak Gibbs states. In particular, we establish the FT in the phase transition regime. These results hold under minimal chaoticity assumptions (expansiveness and specification) and require no ergodicity conditions. They are also valid for systems that are not necessarily invertible and involutions other than time reversal. Further extensions involve asymptotically additive potential sequences and the corresponding weak Gibbs measures. The generality of these results allows to view the FT as a structural facet of the thermodynamic formalism of dynamical systems.

Full statistics of erasure processes: Isothermal adiabatic theory and a statistical Landauer principle

Abstract: We study driven finite quantum systems in contact with a thermal reservoir in the regime in which the system changes slowly in comparison to the equilibration time. The associated isothermal adiabatic theorem allows us to control the full statistics of energy transfers in quasi-static processes. Within this approach, we extend Landauer's Principle on the energetic cost of erasure processes to the level of the full statistics and elucidate the nature of the fluctuations breaking Landauer's bound.

Energy Statistics in Open Harmonic Networks

Abstract: We relate the large time asymptotics of the energy statistics in open harmonic networks to the variance-gamma distribution and prove a full large deviation principle. We consider both Hamiltonian and stochastic dynamics, the later case including electronic RC networks. We compare our theoretical predictions with the experimental data obtained by Ciliberto et al. (Phys. Rev. Lett. 110:180601, 2013).

Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces

Abstract: We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle-Lanford functions, and the exposition is essentially self-contained.

Energy statistics in open harmonic networks

Abstract: We relate the large time asymptotics of the energy statistics in open harmonic networks to the variance-gamma distribution and prove a full Large Deviation Principle. We consider both Hamiltonian and stochastic dynamics, the later case including electronic RC networks. We compare our theoretical predictions with the experimental data obtained by Ciliberto et al. [Phys. Rev. Lett. 110, 180601 (2013)].