Conserved quantity

A measurable quantity that remains constant during a specified evolution or process. In physics, conservation laws often arise from symmetries of the system.

Noether's theorem: A theorem connecting continuous symmetries of a physical action to conserved quantities. It derives conservation laws from symmetries such as time translation and spatial translation.
State space: The set of all possible states of a system, represented by coordinates sufficient to specify its configuration. A conserved quantity is a function on states that stays fixed along allowed evolution.
Energy conservation: The principle that total energy remains constant in an isolated system. Energy is the conserved quantity associated with time-translation symmetry.
Dissipation: The irreversible transfer of organized energy into less useful forms, often through heat or sound. Dissipation makes mechanical energy appear to decrease, while total energy remains conserved.
Time-translation symmetry: The property of a system's laws remaining unchanged when time is shifted by a constant interval. When the action has this symmetry, Noether's theorem yields energy conservation.
Dynamical system: A system whose state changes over time according to specified evolution rules. Conservation is defined relative to the system's particular evolution rules.
Linear momentum: A vector quantity equal to mass times velocity in classical mechanics, generalized in other physical theories. Its total value is conserved in isolated systems with spatial translation symmetry.
Energy conservation in general relativity: The limits and local formulations of energy conservation in curved spacetime, where a global conserved energy may not exist. It shows that conservation can depend on spacetime symmetries and the system's boundaries.
Spatial translation symmetry: The property of a system's laws remaining unchanged when every position is shifted by the same displacement. Its Noether charge is linear momentum.
Invariant: A property or quantity unchanged under a specified transformation or evolution. A conserved quantity is an invariant specifically along the system's time evolution.

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