conservation laws

A law that states that, in a closed system, the whole quantity of something will not enhance or reduce, but exactly remain the same; i.e., its rate of alteration is zero. For physical quantities, it states that something can neither be created nor destroyed. Mathematically specking, if a scalar X is the quantity assumed, then

dX/dt = 0,

or, equivalently,

X = constant.

For a vector field F, the conservation law is written as following

div F = 0;

that is, the vector field F refer to divergence-free everywhere (that has no sources or sinks).

Some particular examples of conservation laws are following:

conservation of mass-energy

The overall mass-energy of closed system remains constant.

conservation of electric charge

The overall electric charge of any closed system remains constant.

Conservation of linear momentum

The overall linear momentum of any closed system remains constant.