Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an underlying microscopic dynamics: the only input required are transport coefficients as functions of thermodynamic variables, which are experimentally accessible. The basic postulates are local equilibrium which allows a hydrodynamic description of the evolution, the Einstein relation among the transport coefficients, and a variational principle defining the out of equilibrium free energy. Associated to the variational principle there is a Hamilton-Jacobi equation satisfied by the free energy, very useful for concrete calculations. Correlations over a macroscopic scale are, in our scheme, a generic property of nonequilibrium states. Correlation functions of any order can be calculated from the free energy functional which is generically a non local functional of thermodynamic variables. Special attention is given to the notion of equilibrium state from the standpoint of nonequilibrium.Comment: 21 page

Price Promotion for Emotional Impact

Managers and academics often think of price promotions merely as incentives that entice consumers to accept offers that they might not have considered otherwise. Yet the prospect of paying a lower price for a product of given quality can also discourage deliberation, in a sense "dumbing down" the purchase encounter by making it less consequential. The authors examine this possibility in a dual-system theory of consumer behavior. Specifically, they argue that price promotion lowers a consumer's motivation to exert mental effort, in which case purchase decisions are guided less by extensive information processing and more by a quicker, easier, strong conditioner of preference: affect. Field data from a large daily deal company and four controlled experiments support this idea and document its implications primarily for product choice, in turn providing insight into the form and cause of brand switching that manufacturers and retailers can leverage to improve the allocation of promotional budgets and category management

Anthropometric features and body composition of young athletes practicing karate at a high and medium competitive level

The aim of the study was to examine the anthropometric features and body composition of athletes practising karate at a high and medium competitive level. Our study was carried out on a sample of 35 subjects practising karate and aged from 16.0 to 32.5 years. This sample was divided into two groups: group 1 (n=14 elite athletes) and group 2 (n=21 amateur athletes). Various anthropometric measurements were taken (weight, height both standing and sitting, diameters, circumferences and skinfold thickness) from which different anthropometric indices were calculated (body mass index, Scelic and Grant indices, arm muscle circumference and area), and the somatotype was then determined. The body composition of each subject was assessed using the skinfold technique and the Jackson-Pollock (J-P) and Sloan-Weir (S-W) equations. The two groups of athletes showed very similar measurements regarding anthropometric characteristics. Only the Scelix index presented a significantly different value in the two groups (49.6±1.3 for group 1 vs. 51.1±1.3 for group 2; p<0.01). Group 1 showed a mesomorphic-ectomorphic somatotype, while the amateur athletes presented a balanced mesomorphic type. Moreover, a lower percentage of fat mass was more frequent in the first group (J-P=8.1±2.4%; S-W=8.9±3.3%) than in the second one (J-P=9.8±1.6%; S-W=11.2±3.7%), although the differences between the two groups were not significant. We conclude that group 1 is characterized by a slightly prominent vertical development of the skeletal frame. This could be an anthropometric characteristic that is best suited to meet the specific functional requirements of this sport. Moreover, both groups of athletes are characterized by a low percentage of fat mass, particularly the elite group

Dynamics and Lax-Phillips scattering for generalized Lamb models

This paper treats the dynamics and scattering of a model of coupled oscillating systems, a finite dimensional one and a wave field on the half line. The coupling is realized producing the family of selfadjoint extensions of the suitably restricted self-adjoint operator describing the uncoupled dynamics. The spectral theory of the family is studied and the associated quadratic forms constructed. The dynamics turns out to be Hamiltonian and the Hamiltonian is described, including the case in which the finite dimensional systems comprises nonlinear oscillators; in this case the dynamics is shown to exist as well. In the linear case the system is equivalent, on a dense subspace, to a wave equation on the half line with higher order boundary conditions, described by a differential polynomial $p(\partial_x)$ explicitely related to the model parameters. In terms of such structure the Lax-Phillips scattering of the system is studied. In particular we determine the incoming and outgoing translation representations, the scattering operator, which turns out to be unitarily equivalent to the multiplication operator given by the rational function $-p(i\kappa)^*/p(i\kappa)$, and the Lax-Phillips semigroup, which describes the evolution of the states which are neither incoming in the past nor outgoing in the future

Cashback is cash forward: delaying a discount to entice future spending

The authors examine purchase behavior in the context of cashback shopping—a novel form of price promotion online where consumers initiate transactions at the website of a cashback company and, after a significant delay, receive the savings promised to them. Specifically, they analyze panel data from a large cashback company and show that, independent of the predictable effect of cashback offers on initial demand, cashback payments (1) increase the probability that consumers make an additional purchase via the website of the cashback company, and (2) increase the size of that purchase. These effects pass several robustness checks. They are also meaningful: at the average values in the data an additional $1.00 in cashback payment increases the likelihood of a future transaction by 0.02$0.32—figures that represent 10.03% of the overall impact of a given promotion. Moreover, the authors find that consumers are more likely to spend the money returned to them at generalists such as department stores than at other retailers. They consider three explanations for these findings, and the leading hypothesis is that consumers fail to treat money as a fungible resource. They also discuss implications for cashback companies and retailers

Long range correlations and phase transition in non-equilibrium diffusive systems

We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the occurrence of a phase transition as they become singular when the system approaches the transition

Lagrangian phase transitions in nonequilibrium thermodynamic systems

In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in nonequilibrium this is not necessarily the case. We show that in nonequilibrium a new type of singularities can appear that are interpreted as phase transitions. In particular, this phenomenon occurs for the one-dimensional boundary driven weakly asymmetric exclusion process when the drift due to the external field is opposite to the one due to the external reservoirs, and strong enough.Comment: 10 pages, 2 figure

Perturbative analysis of disordered Ising models close to criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion implies the infinite differentiability of the free energy but not its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder

Crossover to the KPZ equation

We characterize the crossover regime to the KPZ equation for a class of one-dimensional weakly asymmetric exclusion processes. The crossover depends on the strength asymmetry $an^{2-\gamma}$ ($a,\gamma>0$) and it occurs at $\gamma=1/2$. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if $\gamma\in(1/2,1]$, while for $\gamma=1/2$ it is an energy solution of the KPZ equation. The corresponding crossover for the current of particles is readily obtained.Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012), 813-82