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A conserved quantity is a property or value that remains constant over time in a system even when changes occur in the system. In mathematics , a conserved quantity of a dynamical system is formally defined as a function of the dependent variables , the value of which remains constant along each trajectory of the system.
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge.
Also, conjugate variables are related by Noether's theorem, which states that if the laws of physics are invariant with respect to a change in one of the conjugate variables, then the other conjugate variable will not change with time (i.e. it will be conserved). Conjugate variables in thermodynamics are widely used.
The local conservation of non-gravitational linear momentum and energy in a free-falling reference frame is expressed by the vanishing of the covariant divergence of the stress–energy tensor. Another important conserved quantity, discovered in studies of the celestial mechanics of astronomical bodies, is the Laplace–Runge–Lenz vector.
In physics a conserved current is a current, , that satisfies the continuity equation =.The continuity equation represents a conservation law, hence the name. Indeed, integrating the continuity equation over a volume , large enough to have no net currents through its surface, leads to the conservation law =, where = is the conserved quantity.
According to Noether's theorem, each symmetry of a system is associated a conserved quantity. [1] [2] For example, the rotational invariance of a system implies the conservation of its angular momentum, or spacetime invariance implies the conservation of energy–momentum. In quantum field theory, internal symmetries also result in conserved ...
Meaning SI unit of measure alpha: alpha particle: angular acceleration: radian per second squared (rad/s 2) fine-structure constant: unitless beta: velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian
The purity of a quantum state is conserved under unitary transformations acting on the density matrix in the form †, where U is a unitary matrix. Specifically, it is conserved under the time evolution operator U ( t , t 0 ) = e − i ℏ H ( t − t 0 ) {\displaystyle U(t,t_{0})=e^{{\frac {-i}{\hbar }}H(t-t_{0})}\,} , where H is the ...