Dependence of the fluctuation-dissipation temperature on the choice of observable

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is non-uniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.Comment: 4 pages, 2 figures, final versio

What does economic research tell us about cross-border e-commerce in the EU Digital Single Market? A summary of recent research.

This note presents a non-technical summary of the latest economic research studies on cross-border e-commerce in the EU and elsewhere, and combines this with findings from older research on this subject. It compares online with offline cross-border trade and investigates the differences in drivers and impediments to both. It also looks into research findings regarding consumer motives to shift from offline to online trade and explores possible sources of consumer welfare increase as a result of this shift. Finally, it flags issues for further research. The main purpose of this note is to bring the findings from recent research together in a coherent framework and make it accessible to stakeholders and decision-makers involved in EU policy-making on the Digital Agenda for Europe and the EU Digital Single Market.JRC.J.3-Information Societ

Criticality at finite strain rate in fluidized soft glassy materials

We study the emergence of critical dynamics in the steady shear rheology of fluidized soft glassy materials. Within a mesoscale elasto-plastic model accounting for a shear band instability, we show how an additional noise can induce a transition from phase separated to homogeneous flow, accompanied by critical-like fluctuations of the macroscopic shear rate. Both macroscopic quantities and fluctuations exhibit power law behaviors in the vicinity of this transition, consistent with previous experimental findings on vibrated granular media. Altogether, our results suggest a generic scenario for the emergence of criticality when shear weakening mechanisms compete with a fluidizing noise.Comment: 7 pages, 7 figure

Intensive thermodynamic parameters in nonequilibrium systems

Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system has to satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe nonequilibrium phase coexistence, as illustrated on different models. We finally discuss the issue of the equalization of ITPs when two different systems are put into contact. This issue is closely related to the possibility of measuring the ITPs using a small auxiliary system, in the same way as temperature is measured with a thermometer, and points at one of the major difficulties of nonequilibrium statistical mechanics. In addition, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.Comment: 17 pages, 5 figures; final version, with minor change

On the relevance of disorder in athermal amorphous materials under shear

We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly two types of noise (thermal versus athermal). Within this interpretation framework, we argue that mean-field athermal dynamics can be accounted for by the so-called H{\'e}braud-Lequeux (HL) model, in which the mechanical noise stems explicitly from the plastic activity in the sheared medium. Then, we show that the inclusion of structural disorder, by means of a distribution of yield energy barriers, has no qualitative effect in the HL model, while such a disorder is known to be one of the key ingredients leading kinematically to a finite macroscopic yield stress in other mean-field descriptions, such as the Soft-Glassy-Rheology model. We conclude that the statistical mechanisms at play in the emergence of a macroscopic yield stress, and a complex stationary dynamics at low shear rate, are different in thermal and athermal amorphous systems

Influence of flux balance on the generalized chemical potential in mass transport models

In equilibrium systems, the conservation of the number of particles (or mass) leads to the equalization of the chemical potential throughout the system. Using a non-equilibrium generalization of the notion of chemical potential, we investigate the influence of disorder and of the balance of mass fluxes on the generalized chemical potential in the framework of stochastic mass transport models. We focus specifically on the issue of local mesurements of the chemical potential. We find that while local dynamical disorder does not affect the measurement process, the presence of large-scale geometrical heterogeneities (branching geometry) leads to unequal local measurement results in different points of the system. We interpret these results in terms of mass flux balance, and argue that the conditions for the global definition of the chemical potential still hold, but that local measurements fail to capture the global theoretical value.Comment: 14 pages, 7 figure

Digital music consumption on the Internet: Evidence from clickstream data

The goal of this paper is to analyze the behavior of digital music consumers on the Internet. Using clickstream data on a panel of more than 16,000 European consumers, we estimate the eects of illegal downloading and legal streaming on the legal purchases of digital music. Our results suggest that Internet users do not view illegal downloading as a substitute to legal digital music. Although positive and signicant, our estimated elasticities are essentially zero: a 10% increase in clicks on illegal downloading websites leads to a 0.2% increase in clicks on legal purchases websites. Online music streaming services are found to have a somewhat larger (but still small) eect on the purchases of digital sound recordings, suggesting complementarities between these two modes of music consumption. According to our results, a 10% increase in clicks on legal streaming websites lead to up to a 0.7% increase in clicks on legal digital purchases websites. We nd important cross country dierence in these eects.JRC.J.3-Information Societ

Does online trade live up to the promise of a borderless world? Evidence from the EU Digital Single Market

An important EU Digital Single Market policy objective is to achieve an open and integrated market for online e-commerce in the EU, to make it easy for consumers to go outside their domestic market and shop online in other EU Member States. This study applies a standard gravity model of international trade to Google e-commerce data to estimate the prevalence of home bias in online shopping in the EU. It compares how much EU Member States trade domestically and with other Member States, and how much the EU trades with itself and with the rest of the world. The research confirms the findings of the (offline) international trade literature, according to which there is strong home bias. There is no unambiguous evidence about the strengths or weaknesses of the EU Digital Single Market. Strong intra-EU home bias suggests that online consumers have a tendency to stay in their home country market. Equally strong extra-EU home bias suggests that online consumers who do decide to shop abroad have a tendency to stay in the EU however, rather than going to a non-EU country. There are indications that online home bias is lower in a comparable cross-border trade setting in North America. Data and methodological limitations do not allow a more detailed analysis.JRC.J.3-Information Societ

Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature

The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable independence is deeply related to the uniformity of the phase-space probability distribution on the hypersurfaces of constant energy. This property is shown explicitly on three different stochastic models, where observable-dependence of the fluctuation-dissipation temperature arises only when the uniformity of the phase-space distribution is broken. The first model is an energy transport model on a ring, with biased local transfer rules. In the second model, defined on a fully connected geometry, energy is exchanged with two heat baths at different temperatures, breaking the uniformity of the phase-space distribution. Finally, in the last model, the system is connected to a zero temperature reservoir, and preserves the uniformity of the phase-space distribution in the relaxation regime, leading to an observable-independent temperature.Comment: 15 pages, 7 figure

The drivers and impediments for cross-border e-commerce in the EU

There are no official statistics on international online trade in goods so far. This paper uses a consumer survey to construct a unique matrix of online B2C domestic and cross-border trade in goods between the 27 EU Member States. We compare online and offline trade patterns for similar goods. We find that the standard gravity model performs well in explaining online cross-border trade flows. The model confirms the strong reduction in geographical distance-related trade costs, compared to offline trade. However, the trade costs associated with crossing language barriers increase when moving from offline to online trade. Institutional variables such as online payments facilities and cost-efficiency of parcel delivery systems might play a significant role in cross-border trade and our analysis confirms this. In a linguistically segmented market like the EU, online home market bias remains high compared to bias in offline cross-border trade. We conclude that it is hard to predict at this stage whether regulators could boost online cross-border trade through improvements in legal and financial systems, and parcel delivery infrastructure.JRC.J.3-Information Societ