Classical and Quantum GravityClassical and Quantum Gravity is a peer-reviewed journal that covers all aspects of gravitational physics and the theory of spacetime. Its scope includes: Classical general relativity Applications of relativity Experimental gravitation Cosmology and the early universe Quantum gravity Supergravity, superstrings and supersymmetry Mathematical physics relevant to gravitation The editor-in-chief is Gabriela González at Louisiana State University. The 2018 impact factor is 3.487 according to Journal Citation Reports.
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.
SemigroupIn mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively (just notation, not necessarily the elementary arithmetic multiplication): x·y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y). Associativity is formally expressed as that (x·y)·z = x·(y·z) for all x, y and z in the semigroup.
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.
Asymptotic equipartition propertyIn information theory, the asymptotic equipartition property (AEP) is a general property of the output samples of a stochastic source. It is fundamental to the concept of typical set used in theories of data compression. Roughly speaking, the theorem states that although there are many series of results that may be produced by a random process, the one actually produced is most probably from a loosely defined set of outcomes that all have approximately the same chance of being the one actually realized.
QuotientIn arithmetic, a quotient (from quotiens 'how many times', pronounced ˈkwoʊʃənt) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division), or as a fraction or a ratio (in the case of a general division). For example, when dividing 20 (the dividend) by 3 (the divisor), the quotient is 6 (with a remainder of 2) in the first sense, and (a repeating decimal) in the second sense.
Moufang loopIn mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were introduced by . Smooth Moufang loops have an associated algebra, the Malcev algebra, similar in some ways to how a Lie group has an associated Lie algebra. A Moufang loop is a loop that satisfies the four following equivalent identities for all , , in (the binary operation in is denoted by juxtaposition): These identities are known as Moufang identities.
Universal algebraUniversal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study. Algebraic structure In universal algebra, an algebra (or algebraic structure) is a set A together with a collection of operations on A. An n-ary operation on A is a function that takes n elements of A and returns a single element of A.
Quotient space (topology)In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes). In other words, a subset of a quotient space is open if and only if its under the canonical projection map is open in the original topological space.
History of entropyThe concept of entropy developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work. Early heat-powered engines such as Thomas Savery's (1698), the Newcomen engine (1712) and the Cugnot steam tricycle (1769) were inefficient, converting less than two percent of the input energy into useful work output; a great deal of useful energy was dissipated or lost.
