Statistical mechanicsIn physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, and neuroscience.
Ideal gas lawThe ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form: where , and are the pressure, volume and temperature respectively; is the amount of substance; and is the ideal gas constant.
Isolated systemIn physical science, an isolated system is either of the following: a physical system so far removed from other systems that it does not interact with them. a thermodynamic system enclosed by rigid immovable walls through which neither mass nor energy can pass. Though subject internally to its own gravity, an isolated system is usually taken to be outside the reach of external gravitational and other long-range forces.
Thermodynamic systemA thermodynamic system is a body of matter and/or radiation, considered as separate from its surroundings, and studied using the laws of thermodynamics. Thermodynamic systems may be isolated, closed, or open. An isolated system exchanges no matter or energy with its surroundings, whereas a closed system does not exchange matter but may exchange heat and experience and exert forces. An open system can interact with its surroundings by exchanging both matter and energy.
SystemA system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity.
Closed systemA closed system is a natural physical system that does not allow transfer of matter in or out of the system, although - in the contexts of physics, chemistry, engineering, etc. - the transfer of energy (e.g. as work or heat) is allowed. In nonrelativistic classical mechanics, a closed system is a physical system that doesn't exchange any matter with its surroundings, and isn't subject to any net force whose source is external to the system. A closed system in classical mechanics would be equivalent to an isolated system in thermodynamics.
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.
Identical particlesIn quantum mechanics, identical particles (also called indistinguishable or indiscernible particles) are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, elementary particles (such as electrons), composite subatomic particles (such as atomic nuclei), as well as atoms and molecules. Quasiparticles also behave in this way.
Drainage divideA drainage divide, water divide, ridgeline, watershed, water parting or height of land is elevated terrain that separates neighboring drainage basins. On rugged land, the divide lies along topographical ridges, and may be in the form of a single range of hills or mountains, known as a dividing range. On flat terrain, especially where the ground is marshy, the divide may be difficult to discern. A triple divide is a point, often a summit, where three drainage basins meet.
PropertyProperty is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, redefine, rent, mortgage, pawn, sell, exchange, transfer, give away, or destroy it, or to exclude others from doing these things, as well as to perhaps abandon it; whereas regardless of the nature of the property, the owner thereof has the right to properly use it under the granted property rights.
Continental divideA continental divide is a drainage divide on a continent such that the drainage basin on one side of the divide feeds into one ocean or sea, and the basin on the other side either feeds into a different ocean or sea, or else is endorheic, not connected to the open sea. Every continent on earth except Antarctica (which has no known significant, definable free-flowing surface rivers) has at least one continental drainage divide; islands, even small ones like Killiniq Island on the Labrador Sea in Canada, may also host part of a continental divide or have their own island-spanning divide.
Property lawProperty law is the area of law that governs the various forms of ownership in real property (land) and personal property. Property refers to legally protected claims to resources, such as land and personal property, including intellectual property. Property can be exchanged through contract law, and if property is violated, one could sue under tort law to protect it. The concept, idea or philosophy of property underlies all property law.
Continental Divide of the AmericasThe Continental Divide of the Americas (also known as the Great Divide, the Western Divide or simply the Continental Divide; Divisoria continental de América, Gran Divisoria) is the principal, and largely mountainous, hydrological divide of the Americas. The Continental Divide extends from the Bering Strait to the Strait of Magellan, and separates the watersheds that drain into the Pacific Ocean from those river systems that drain into the Atlantic and Arctic Ocean, including those that drain into the Gulf of Mexico, the Caribbean Sea, and Hudson Bay.
Personal propertyPersonal property is property that is movable. In common law systems, personal property may also be called chattels or personalty. In civil law systems, personal property is often called movable property or movables—any property that can be moved from one location to another. Personal property can be understood in comparison to real estate, immovable property or real property (such as land and buildings). Movable property on land (larger livestock, for example) was not automatically sold with the land, it was "personal" to the owner and moved with the owner.
Ergodic hypothesisIn physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equiprobable over a long period of time. Liouville's theorem states that, for a Hamiltonian system, the local density of microstates following a particle path through phase space is constant as viewed by an observer moving with the ensemble (i.
Real propertyIn English common law, real property, real estate, immovable property or, solely in the US and Canada, realty, is land which is the property of some person and all structures (also called improvements or fixtures) integrated with or affixed to the land, including crops, buildings, machinery, wells, dams, ponds, mines, canals, roads, and other things. The term is historic, arising from the now-discontinued form of action, which distinguished between real property disputes and personal property disputes.
ParticleIn the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and molecules, to macroscopic particles like powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion.
Ergodic theoryErgodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc.
Elementary particleIn particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles, twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons.
ErgodicityIn mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the trajectory of a "typical" point. Equivalently, a sufficiently large collection of random samples from a process can represent the average statistical properties of the entire process.
