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Christian Maes - One of the best experts on this subject based on the ideXlab platform.
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An update on nonequilibrium Linear Response
New Journal of Physics, 2013Co-Authors: Marco Baiesi, Christian MaesAbstract:The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium Linear Response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second "probabilistic" approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to Linear Response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition.
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an update on the nonequilibrium Linear Response
New Journal of Physics, 2013Co-Authors: Marco Baiesi, Christian MaesAbstract:The unique fluctuation–dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium Linear Response formulae. Their most traditional approach is ‘analytic’, which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work even when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second ‘probabilistic’ approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to Linear Response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition.
Marco Baiesi - One of the best experts on this subject based on the ideXlab platform.
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An update on nonequilibrium Linear Response
New Journal of Physics, 2013Co-Authors: Marco Baiesi, Christian MaesAbstract:The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium Linear Response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second "probabilistic" approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to Linear Response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition.
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an update on the nonequilibrium Linear Response
New Journal of Physics, 2013Co-Authors: Marco Baiesi, Christian MaesAbstract:The unique fluctuation–dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium Linear Response formulae. Their most traditional approach is ‘analytic’, which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work even when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second ‘probabilistic’ approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to Linear Response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition.
Frank De Proft - One of the best experts on this subject based on the ideXlab platform.
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Conceptual DFT: chemistry from the Linear Response function.
Chemical Society reviews, 2014Co-Authors: Paul Geerlings, Stijn Fias, Zino Boisdenghien, Frank De ProftAbstract:Within the context of reactivity descriptors known in conceptual DFT, the Linear Response function (χ(r,r′)) remained nearly unexploited. Although well known, in its time dependent form, in the solid state physics and time-dependent DFT communities the study of the “chemistry” present in the kernel was, until recently, relatively unexplored. The evaluation of the Linear Response function as such and its study in the time independent form are highlighted in the present review. On the fundamental side, the focus is on the approaches of increasing complexity to compute and represent χ(r,r′), its visualisation going from plots of the unintegrated χ(r,r′) to an atom condensed matrix. The study on atoms reveals its physical significance, retrieving atomic shell structure, while the results on molecules illustrate that a variety of chemical concepts are retrieved: inductive and mesomeric effects, electron delocalisation, aromaticity and anti-aromaticity, σ and π aromaticity,…. The applications show that the chemistry of aliphatic (saturated and unsaturated) chains, saturated and aromatic/anti-aromatic rings, organic, inorganic or metallic in nature, can be retrieved via the Linear Response function, including the variation of the electronic structure of the reagents along a reaction path. The connection of the Linear Response function with the concept of nearsightedness and the alchemical derivatives is also highlighted.
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Analysis of aromaticity in planar metal systems using the Linear Response kernel.
The journal of physical chemistry. A, 2013Co-Authors: Stijn Fias, Paul Geerlings, Zino Boisdenghien, Thijs Stuyver, Martha Audiffred, Gabriel Merino, Frank De ProftAbstract:The Linear Response kernel is used to gain insight into the aromatic behavior of the less classical metal aromatic E42– and CE42– (E = Al, Ga) clusters. The effect of the systematic replacement of the aluminum atoms in Al42– and CAl42– by germanium atoms is studied using, Al3Ge–, Al2Ge2, AlGe3+, Ge42+, CAl3Ge–, CAl2Ge2, CAlGe3+, and CGe42+. The results are compared with the values of the delocalization index (δ1,3) and nucleus independent chemical shifts (NICSzz). Unintegrated plots of the Linear Response, computed for the first time on molecules, are used to analyze the delocalization in these clusters. All aromaticity indices studied, the Linear Response, δ1,3, and NICSzz, predict that the systems with a central carbon are less aromatic than the systems without a central carbon atom. Also, the Linear Response is more pronounced in the σ-electron density than in the π-density, pointing out that the systems are mainly σ-aromatic.
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σ, π aromaticity and anti-aromaticity as retrieved by the Linear Response kernel
Physical Chemistry Chemical Physics, 2013Co-Authors: Stijn Fias, Paul Geerlings, Paul W. Ayers, Frank De ProftAbstract:The chemical importance of the Linear Response kernel from conceptual Density Functional Theory (DFT) is investigated for some σ and π aromatic and anti-aromatic systems. The effect of the ring size is studied by looking at some well known aromatic and anti-aromatic molecules of different sizes, showing that the Linear Response is capable of correctly classifying and quantifying the aromaticity for five- to eight-membered aromatic and anti-aromatic molecules. The splitting of the Linear Response in σ and π contributions is introduced and its significance is illustrated using some σ-aromatic molecules. The Linear Response also correctly predicts the aromatic transition states of the Diels–Alder reaction and the acetylene trimerisation and shows the expected behavior along the reaction coordinate, proving that the method is accurate not only at the minimum of the potential energy surface, but also in non-equilibrium states. Finally, the reason for the close correlation between the Linear Response and the Para Delocalisation Index (PDI), found in previous and the present study, is proven mathematically. These results show the Linear Response to be a reliable DFT-index to probe the σ and π aromaticity or anti-aromaticity of a broad range of molecules.
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The Linear Response kernel of conceptual DFT as a measure of aromaticity
Physical chemistry chemical physics : PCCP, 2012Co-Authors: Nick Sablon, Frank De Proft, Miquel Solà, Paul GeerlingsAbstract:We continue a series of papers in which the chemical importance of the Linear Response kernel χ(r,r′) of conceptual DFT is investigated. In previous contributions (J. Chem. Theory Comput. 2010, 6, 3671; J. Phys. Chem. Lett. 2010, 1, 1228; Chem. Phys. Lett. 2010, 498, 192), two computational methodologies were presented and it was observed that the Linear Response kernel could serve as a measure of electron delocalisation, discerning inductive, resonance and hyperconjugation effects. This study takes the analysis one step further, linking the Linear Response kernel to the concept of aromaticity. Based on a detailed analysis of a series of organic and inorganic (poly)cyclic molecules, we show that the atom-condensed Linear Response kernel discriminates between aromatic and non-aromatic systems. Moreover, a new quantitative measure of aromaticity, termed the para Linear Response (PLR) index, is introduced. Its definition was inspired by the recent work published around the para delocalisation index (PDI). Both indices are shown to correlate very well, which emphasises the Linear Response kernel's value in the theoretical description of aromaticity.
Benoît Saussol - One of the best experts on this subject based on the ideXlab platform.
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Linear Response for random dynamical systems
Advances in Mathematics, 2020Co-Authors: Wael Bahsoun, Marks Ruziboev, Benoît SaussolAbstract:Abstract We study for the first time Linear Response for random compositions of maps, chosen independently according to a distribution P . We are interested in the following question: how does an absolutely continuous stationary measure (acsm) of a random system change when P changes smoothly to P e ? For a wide class of one dimensional random maps, we prove differentiability of acsm with respect to e; moreover, we obtain a Linear Response formula. Our results cover random maps whose transfer operator does not necessarily admit a spectral gap. We apply our results to iid compositions, with respect to various distributions P e , of uniformly expanding circle maps, Gauss-Renyi maps (random continued fractions) and Pomeau-Manneville maps. Our results yield an exact formula for the invariant density of random continued fractions; while for Pomeau-Manneville maps our results provide a precise relation between their Linear Response under certain random perturbations and their Linear Response under deterministic perturbations.
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Linear Response for random dynamical systems.
arXiv: Dynamical Systems, 2017Co-Authors: Wael Bahsoun, Marks Ruziboev, Benoît SaussolAbstract:We study for the first time Linear Response for random compositions of maps, chosen independently according to a distribution $\PP$. We are interested in the following question: how does an absolutely continuous stationary measure (acsm) of a random system change when $\PP$ changes smoothly to $\PP_{\eps}$? For a wide class of one dimensional random maps, we prove differentiability of acsm with respect to $\eps$; moreover, we obtain a Linear Response formula. We apply our results to iid compositions, with respect to various distributions $\PP_{\eps}$, of uniformly expanding circle maps, Gauss-R\'enyi maps (random continued fractions) and Pomeau-Manneville maps. Our results yield an exact formula for the invariant density of random continued fractions; while for Pomeau-Manneville maps our results provide a precise relation between their Linear Response under certain random perturbations and their Linear Response under deterministic perturbations.
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Linear Response in the intermittent family: Differentiation in a weighted $C^0$-norm
Discrete and Continuous Dynamical Systems, 2016Co-Authors: Wael Bahsoun, Benoît SaussolAbstract:We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly expanding system to a uniformly expanding one, and on showing how the Linear Response formula of the non-uniformly expanding system is inherited from the Linear Response formula of the induced one. We apply this general technique to interval maps with a neutral fixed point (Pomeau-Manneville maps) to prove differentiability of the corresponding SRB measure. Our work covers systems that admit a finite SRB measure and it also covers systems that admit an infinite SRB measure. In particular, we obtain a Linear Response formula for both finite and infinite SRB measures. To the best of our knowledge, this is the first work that contains a Linear Response result for infinite measure preserving systems.
Jianhui Wang - One of the best experts on this subject based on the ideXlab platform.
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endoreversible quantum heat engines in the Linear Response regime
Physical Review E, 2017Co-Authors: Honghui Wang, Jianhui WangAbstract:We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the Linear Response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a Linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the Linear Response regime.
