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Concept

Limite thermodynamique

Résumé

En physique statistique, la limite thermodynamique est la limite mathématique conjointe où :

le nombre de particules N du système considéré tend vers l'infini ;
le volume V du système considéré tend vers l'infini ;
la densité de particules \rho = N/V du système considéré reste constante.

Dans le problème thermodynamique de la réunion de systèmes disjoints, on peut aussi voir la limite thermodynamique comme étant le passage d'effets de surface prépondérants à des effets de volume prépondérants. Ainsi, quand cette limite est atteinte, on retrouve la pertinence de la notion d'extensivité par exemple. Articles connexes

Physique statistique
Extensif

Bibliographie

Roger Balian ; Du microscopique au macroscopique - Cours de physique statistique de l'École Polytechnique, vol 1, Ellipse (1982), .
Elliott Lieb ; The Stability of Matter: from Atoms to Stars, Springer-Verlag (1991), .

Catégorie:Physique statistiq

Source officielle

https://fr.wikipedia.org/wiki/Limite_thermodynamique

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This course presents an introduction to statistical mechanics geared towards materials scientists. The concepts of macroscopic thermodynamics will be related to a microscopic picture and a statistical interpretation. Lectures and exercises will be complemented with hands-on simulation projects.

Le but du cours de Physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de prévoir quantitativement les conséquences de ces phénomènes avec des outils théoriques appropriés.

This course builds upon the underlying theory in thermodynamics, reaction kinetics, and transport and applies these methods to electrosynthesis, fuel cell, and battery applications. Special focus is placed on addressing current challenges in state-of-the-art energy storage and conversion devices.

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Level crossings induced by a longitudinal coupling in the transverse field Ising chain

Frédéric Mila, Grégoire Vionnet

We study the effect of antiferromagnetic longitudinal coupling on the one-dimensional transverse field Ising model with nearest-neighbor couplings. In the topological phase where, in the thermodynamic limit, the ground state is twofold degenerate, we show that, for a finite system of N sites, the longitudinal coupling induces N level crossings between the two lowest-lying states as a function of the field. We also provide strong arguments suggesting that these N level crossings all appear simultaneously as soon as the longitudinal coupling is switched on. This conclusion is based on perturbation theory and a mapping of the problem onto the open Kitaev chain, for which we write down the complete solution in terms of Majorana fermions.

2017

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, ,

Amorphous materials exhibit complex material properties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while they start to yield above a critical stress sigma(c). A key quantity controlling plasticity which is, however, hard to measure is the density P(x) of weak spots, where x is the additional stress required for local plastic failure. In the thermodynamic limit P(x) similar to x(theta) is singular at x = 0 in the solid phase below the yield stress sigma(c). This singularity is related to the presence of system spanning avalanches of plastic events. Here we address the question if the density of weak spots and the flow properties of a material can be determined from the geometry of an amorphous structure alone. We show that a vertex model for cell packings in tissues exhibits the phenomenology of plastic amorphous systems. As the yield stress is approached from above, the strain rate vanishes and the avalanches size S and their duration tau diverge. We then show that in general, in materials where the energy functional depends on topology, the value x is proportional to the length L of a bond that vanishes in a plastic event. For this class of models P(x) is therefore readily measurable from geometry alone. Applying this approach to a quantification of the cell packing geometry in the developing wing epithelium of the fruit fly, we find that in this tissue P(L) exhibits a power law with exponents similar to those found numerically for a vertex model in its solid phase. This suggests that this tissue exhibits plasticity and non-linear material properties that emerge from collective cell behaviors and that these material properties govern developmental processes. Our approach based on the relation between topology and energetics suggests a new route to outstanding questions associated with the yielding transition.

IOP PUBLISHING LTD2021

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Deterministic Motion of the Controversial Piston in the Thermodynamic Limit

Christian Gruber, Séverine Pache

Springer, Kluwer Academic Publishers-Plenum Publishers2002

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