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.
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).
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.
FranceFrance (fʁɑ̃s), officially the French Republic (République française ʁepyblik fʁɑ̃sɛz), is a country located primarily in Western Europe. It also includes overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans, giving it one of the largest discontiguous exclusive economic zones in the world. Its metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean.
BordeauxBordeaux (bɔːrˈdoʊ , bɔʁdo; Gascon Bordèu buɾˈðɛw; Bordele) is a city on the river Garonne in the Gironde department, Southwestern France. A port city, it is the capital of the Nouvelle-Aquitaine region, as well as the prefecture of the Gironde department. Its inhabitants are called "Bordelais" (masculine) or "Bordelaises" (feminine). The term "Bordelais" may also refer to the city and its surrounding region.
LausanneLausanne (loʊˈzæn , USalsoloʊˈzɑːn , lɔzan; Losena lɔˈzəna) is the capital and largest city of the Swiss French-speaking canton of Vaud. It is a hilly city situated on the shores of Lake Geneva, about halfway between the Jura Mountains and the Alps, and facing the French town of Évian-les-Bains across the lake. Lausanne is located northeast of Geneva, the nearest major city. The municipality of Lausanne has a population of about 140,000, making it the fourth largest city in Switzerland after Basel, Geneva, and Zurich, with the entire agglomeration area having about 420,000 inhabitants (as of January 2019).
GenevaGeneva (dʒəˈniːvə ; Genève ʒənɛv) is the second-most populous city in Switzerland (after Zürich) and the most populous city of Romandy, the French-speaking part of Switzerland. Situated in the south west of the country, where the Rhône exits Lake Geneva, it is the capital of the Republic and Canton of Geneva, and a center for international diplomacy. The city of Geneva (ville de Genève) had a population of 203,951 in 2020 (Jan. estimate) within its small municipal territory of , but the Canton of Geneva (the city and its closest Swiss suburbs and exurbs) had a population of 504,128 (Jan.
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.
Pierre Louis MaupertuisPierre Louis Moreau de Maupertuis (ˌmoʊpərˈtwiː; mopɛʁtɥi; 1698 – 27 July 1759) was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Prussian Academy of Science, at the invitation of Frederick the Great. Maupertuis made an expedition to Lapland to determine the shape of the Earth. He is often credited with having invented the principle of least action; a version is known as Maupertuis's principle – an integral equation that determines the path followed by a physical system.
