classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to decrease in...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a divisor of | G | {\displaystyle...

In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

N\hookrightarrow W} are homotopy equivalences. The h-cobordism theorem gives sufficient conditions for an h-cobordism to be trivial, i.e., to be C-isomorphic...

In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, return...

In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented...

Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h :...

The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate...

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct...

1982 by William Wootters and Wojciech H. Zurek as well as Dennis Dieks the same year). The aforementioned theorems do not preclude the state of one system...

that emerged in the first half of the 20th century. The theorem was first proved by Marshall H. Stone. Stone was led to it by his study of the spectral...

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...

In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients...

In mathematics, the inverse function theorem is a theorem that asserts that, if a real function f has a continuous derivative near a point where its derivative...

\left({\frac {P(X(t)=i)}{\pi _{i}}}\right),} is monotonically increasing (H-theorem). This is a consequence of the convergence to the equilibrium distribution...

increasing according to the second law of thermodynamics, Boltzmann’s H-theorem used equations, which assumed a system (for example, a gas) was isolated...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region K {\displaystyle...

In calculus, the squeeze theorem (also known as the sandwich theorem, among other names) is a theorem regarding the limit of a function that is bounded...

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing...

transform. Marshall H. Stone considerably generalized the theorem and simplified the proof. His result is known as the Stone–Weierstrass theorem. The Stone–Weierstrass...

fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R...

introduced for collisions by Ludwig Boltzmann. In 1872, he proved his H-theorem using this principle. The arguments in favor of this property are founded...