Category: Statistical mechanics theorems

Fluctuation theorem
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e.
Crooks fluctuation theorem
The Crooks fluctuation theorem (CFT), sometimes known as the Crooks equation, is an equation in statistical mechanics that relates the work done on a system during a non-equilibrium transformation to
Bohr–Van Leeuwen theorem
The Bohr–Van Leeuwen theorem states that when statistical mechanics and classical mechanics are applied consistently, the of the magnetization is always zero. This makes magnetism in solids solely a q
Stability of matter
Stability of matter refers to the problem of showing rigorously that a large number of charged quantum particles can coexist and form macroscopic objects, like ordinary matter. The first proof was pro
Mermin–Wagner theorem
In quantum field theory and statistical mechanics, the Mermin–Wagner theorem (also known as Mermin–Wagner–Hohenberg theorem, Mermin–Wagner–Berezinskii theorem, or Coleman theorem) states that continuo
Elitzur's theorem
In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant und
Spin–statistics theorem
In quantum mechanics, the spin–statistics theorem relates the intrinsic spin of a particle (angular momentum not due to the orbital motion) to the particle statistics it obeys. In units of the reduced
Triangulation sensing
No description available.
Fluctuation-dissipation theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given t
Liouville's theorem (Hamiltonian)
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. It asserts that the phase-space distributio
Lee–Yang theorem
In statistical mechanics, the Lee–Yang theorem states that if partition functions of certain models in statistical field theory with ferromagnetic interactions are considered as functions of an extern
In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity H (defined below) in a nearly-ideal gas of molecules. As t
Helmholtz theorem (classical mechanics)
The Helmholtz theorem of classical mechanics reads as follows: Let be the Hamiltonian of a one-dimensional system, where is the kinetic energy and is a "U-shaped" potential energy profile which depend
Equipartition theorem
In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipart
No-communication theorem
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not pos