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.
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).
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.
Notre-Dame de ParisNotre-Dame de Paris (nɔtʁ(ə) dam də paʁi; meaning "Our Lady of Paris"), referred to simply as Notre-Dame, is a medieval Catholic cathedral on the Île de la Cité (an island in the Seine River), in the 4th arrondissement of Paris, France. The cathedral, dedicated to the Virgin Mary, is considered one of the finest examples of French Gothic architecture. Several attributes set it apart from the earlier Romanesque style, particularly its pioneering use of the rib vault and flying buttress, its enormous and colourful rose windows, and the naturalism and abundance of its sculptural decoration.
PanthéonThe Panthéon (pɑ̃.te.ɔ̃, from the Classical Greek word πάνθειον, , '[temple] to all the gods') is a monument in the 5th arrondissement of Paris, France. It stands in the Latin Quarter, atop the Montagne Sainte-Geneviève, in the centre of the Place du Panthéon, which was named after it. The edifice was built between 1758 and 1790, from designs by Jacques-Germain Soufflot, at the behest of King Louis XV of France; the king intended it as a church dedicated to Saint Genevieve, Paris's patron saint, whose relics were to be housed in the church.
