Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle

An Extension of the Fluctuation Theorem

Heat fluctuations are studied in a dissipative system with both mechanical and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extended stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and white

Loneliness Across the Life Span

Most people have experienced loneliness and have been able to overcome it to reconnect with other people. In the current review, we provide a life-span perspective on one component of the evolutionary theory of loneliness—a component we refer to as the reaffiliation motive (RAM). The RAM represents the motivation to reconnect with others that is triggered by perceived social isolation. Loneliness is often a transient experience because the RAM leads to reconnection, but sometimes this motivation can fail, leading to prolonged loneliness. We review evidence of how aspects of the RAM change across development and how these aspects can fail for different reasons across the life span. We conclude with a discussion of age-appropriate interventions that may help to alleviate prolonged lonelines

Extended twin study of alcohol use in Virginia and Australia

Drinking alcohol is a normal behavior in many societies, and prior studies have demonstrated it has both genetic and environmental sources of variation. Using two very large samples of twins and their first-degree relatives (Australia ≈ 20,000 individuals from 8,019 families; Virginia ≈ 23,000 from 6,042 families), we examine whether there are differences: (1) in the genetic and environmental factors that influence four interrelated drinking behaviors (quantity, frequency, age of initiation, and number of drinks in the last week), (2) between the twin-only design and the extended twin design, and (3) the Australian and Virginia samples. We find that while drinking behaviors are interrelated, there are substantial differences in the genetic and environmental architectures across phenotypes. Specifically, drinking quantity, frequency, and number of drinks in the past week have large broad genetic variance components, and smaller but significant environmental variance components, while age of onset is driven exclusively by environmental factors. Further, the twin-only design and the extended twin design come to similar conclusions regarding broad-sense heritability and environmental transmission, but the extended twin models provide a more nuanced perspective. Finally, we find a high level of similarity between the Australian and Virginian samples, especially for the genetic factors. The observed differences, when present, tend to be at the environmental level. Implications for the extended twin model and future directions are discussed

Infinite-dimensional Compact Quantum Semigroup

In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra $\mathcal{T}$. The existence of a subalgebra, isomorphic to the algebra of regular Borel's measures on a circle with convolution product, in the dual algebra $\mathcal{T}^*$ is shown. The existence of Haar functionals in the dual algebra and in the above-mentioned subalgebra is proved. Also we show the connection between $\mathcal{T}$ and the structure of weak Hopf algebra.Comment: 17 page

Non-equilibrium work relations

This is a brief review of recently derived relations describing the behaviour of systems far from equilibrium. They include the Fluctuation Theorem, Jarzynski's and Crooks' equalities, and an extended form of the Second Principle for general steady states. They are very general and their proofs are, in most cases, disconcertingly simple.Comment: Brief Summer School Lecture Note

On the entropy production of time series with unidirectional linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are only uncorrelated but not statistically independent of the future. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we show that such a link also exists for the above unidirectional linearity. We study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited to the forward-time conditional probabilities, but not to the backward-time conditionals. The reason for this asymmetry between past and future is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependencies afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward conditionals to the minimal amount of entropy generation.Comment: 16 page

Posterior probability and fluctuation theorem in stochastic processes

A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via the Bayes theorem. In usual fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem adequately recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when adequate assumptions are employed.Comment: 4 page