Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Sibling caringscapes: time–space practices of caring within youth-headed households in Tanzania and Uganda

This paper investigates the time–space practices of young people caring for their siblings in youthheaded households affected by AIDS in Tanzania and Uganda. Based on qualitative exploratory research with young people heading households, their siblings, NGO workers and community members, the article develops the notion of sibling ‘caringscapes’ to analyse young people’s everyday practices and caring pathways through time and space. Participatory time-use data reveals that older siblings of both genders regularly undertake substantial caring tasks at the very high end of the caregiving continuum. Drawing on rhythmanalysis, the paper explores how young people negotiate emotional geographies and temporalities of caring. The competing rhythms of bodies, schooling, work and seasonal agricultural production can result in ‘arrhythmia’ and time scarcity, which has detrimental effects on young people’s health, education,future employment prospects and mobility. Young people’s lifecourse transitions are shaped to a large extent by their caring responsibilities, resulting in some young people remaining in a liminal position for considerable periods, unable to make ‘successful’ transitions to adulthood. Despite structural constraints,however, young people are able to exercise some autonomy over their caring pathways and lifecourse transitions. The research sheds light on the ways that individuals embody the practices, routines and rhythms of everyday life and exercise agency within highly restricted broader landscapes of care.

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

The SV2A ligand levetiracetam inhibits presynaptic Ca2+ channels via an intracellular pathway

Levetiracetam (LEV) is a prominent antiepileptic drug (AED) which binds to neuronal synaptic vesicle glycoprotein 2A (SV2A) protein and has reported effects on ion channels, but retains a poorly-defined mechanism of action. Here, we investigate inhibition of voltage-dependent Ca2+ (CaV) channels as a potential mechanism by which LEV imparts effects on neuronal activity. We used electrophysiological methods to investigate the effects of LEV on cholinergic synaptic transmission and CaV channel activity in superior cervical ganglion neurons (SCGNs). In parallel, we investigated effects of the LEV ‘inactive’ R-enantiomer, UCB L060. Thus, LEV, but not UCB L060 (each 100 μM), inhibited synaptic transmission between SCGNs in long-term culture in a time-dependent manner, significantly reducing excitatory postsynaptic potentials (EPSP) following ≥30 min application. In isolated SCGNs, LEV pretreatment (≥1 h), but not acute (5 min) application, significantly inhibited whole-cell IBa amplitude. In current clamp recordings, LEV reduced the amplitude of the afterhyperpolarizing potential (AHP) in a Ca2+-dependent manner, but also increased action potential (AP) latency in a Ca2+-independent manner, suggesting further mechanisms associated with reduced excitability. Intracellular LEV application (4-5 min) caused a rapid inhibition of IBa amplitude to an extent comparable to that seen following extracellular LEV pretreatment ( ≥ 1 h). Neither pretreatment nor intracellular application of UCB L060 produced any inhibitory effects on IBa amplitude. These results identify a stereospecific intracellular pathway by which LEV inhibits presynaptic CaV channels; resultant reductions in neuronal excitability are proposed to contribute to the anticonvulsant effects of LEV.