Grand canonical ensembleIn statistical mechanics, the grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that are in thermodynamic equilibrium (thermal and chemical) with a reservoir. The system is said to be open in the sense that the system can exchange energy and particles with a reservoir, so that various possible states of the system can differ in both their total energy and total number of particles.
CambraiCambrai (USkæmˈbreɪ,_kɑ̃ˈ-, kɑ̃bʁɛ; Kimbré; Kamerijk), formerly Cambray and historically in English Camerick or Camericke, is a city in the Nord department and in the Hauts-de-France region of France on the Scheldt river, which is known locally as the Escaut river. A sub-prefecture of the department, Cambrai is a town which had 32,501 inhabitants in 2018. It is in the heart of the urban unit of Cambrai with 46,772 inhabitants. Its functional area, a more extensive range, included 94,576 inhabitants in 2018.
Microcanonical ensembleIn statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system does not change with time. The primary macroscopic variables of the microcanonical ensemble are the total number of particles in the system (symbol: N), the system's volume (symbol: V), as well as the total energy in the system (symbol: E).
Canonical ensembleIn statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. The system can exchange energy with the heat bath, so that the states of the system will differ in total energy. The principal thermodynamic variable of the canonical ensemble, determining the probability distribution of states, is the absolute temperature (symbol: T).
Ensemble (mathematical physics)In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system. The concept of an ensemble was introduced by J. Willard Gibbs in 1902.
StrasbourgStrasbourg (UKˈstræzbɜːrɡ, USˈstrɑːsbʊərɡ,ˈstrɑːz-,-bəːrɡ, stʁasbuʁ; Straßburg ˈʃtʁaːsbʊʁk; Strossburi ˈʃd̥ʁɔːsb̥uʁi, Strossburig ˈʃd̥ʁɔːsb̥uʁiɡ̊) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the European Parliament. Located at the border with Germany in the historic region of Alsace, it is the prefecture of the Bas-Rhin department. In 2020, the city proper had 290,576 inhabitants and both the Eurométropole de Strasbourg (Greater Strasbourg) and the Arrondissement of Strasbourg had 511,552 inhabitants.
BrusselsBrussels (Bruxelles bʁysɛl or bʁyksɛl; Brussel ˈbrʏsəl), officially the Brussels-Capital Region (Région de Bruxelles-Capitale; Brussels Hoofdstedelijk Gewest), is a region of Belgium comprising 19 municipalities, including the City of Brussels, which is the capital of Belgium. The Brussels-Capital Region is located in the central portion of the country and is a part of both the French Community of Belgium and the Flemish Community, but is separate from the Flemish Region (within which it forms an enclave) and the Walloon Region.
ParisParis (ˈpærɪs; paʁi) is the capital and most populous city of France, with an official estimated population of 2,102,650 residents as of 1 January 2023 in an area of more than , making it the fourth-most populated city in the European Union as well as the 30th most densely populated city in the world in 2022. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, culture, fashion, gastronomy and many areas.
LuxembourgLuxembourg (ˈlʌksəmbɜːrɡ ; Lëtzebuerg ˈlətsəbuəɕ; Luxembourg lyksɑ̃buʁ; Luxemburg ˈlʊksm̩bʊʁk), officially the Grand Duchy of Luxembourg, is a small landlocked country in Western Europe. It borders Belgium to the west and north, Germany to the east, and France to the south. Its capital and most populous city, Luxembourg, is one of the four institutional seats of the European Union (together with Brussels, Frankfurt, and Strasbourg) and the seat of several EU institutions, notably the Court of Justice of the European Union, the highest judicial authority.
AmiensAmiens (English: æˈmjæ̃ or ˈæmiənz ; amjɛ̃; Anmien, Anmiens or Anmyin) is a city and commune in northern France, located north of Paris and south-west of Lille. It is the capital of the Somme department in the region of Hauts-de-France and had a population of 135,429, as of 2021. A central landmark of the city is Amiens Cathedral, the largest Gothic cathedral in France. Amiens also has one of the largest university hospitals in France, with a capacity of 1,200 beds.
