Conservation of Extensive Quantities Thermodynamic quantities are usually divided into two categories: extensive and intensive. The extensive category is sometimes modified to be an extensive density measured relative to unit mass or volume but except for entropy they are usually assumed to follow some kind of conservation law; simply speaking: what goes in, goes out. The conservation law holds unconditionally, locally and globally, for both mass and electric charge, and also in a somewhat more complicated form per species in chemical reactions. It also holds for volume transfer, but it is less clear to me what would extensivity and conservation mean for surface area although surface tension is its unambiguous intensive conjugate.
While both electric and magnetic dipole moments are additive extensive when their vectorial nature is taken into account, it is not clear to me at all how electric (or macroscopic magnetic) dipole moment is conserved thermodynamically speaking. Ultimately, of course, total charge is 0 in a large enough experimental volume in which everything is included and then one can say that, since electric dipoles are generated by opposing charges being pulled apart, including those generating the external bias field, the total dipole moment should be conserved. But is this really the case, and how could that be proved from the laws electrostatics or magnetostatics? Is an electrochemical battery an example of electric dipole non-conservation?
Are surface area and dipole moments indeed extensive but non-conservative, and are there other similar quantities or, in fact, there is some conservation law that would hold for any of them except for entropy?
 A: Extensive means additive, conserved means that in a system prevented from exchanging that property with the surroundings their sum is fixed regardless of the process that is taking place. Conserved quantities are extensive but the opposite is not true.

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*Example 1 Energy is extensive and is conserved.


*Example 2 Kinetic energy is extensive but not conserved (it can be converted to other forms).


*Example 3 Surface area is extensive but not conserved. The total surface area of two liquid droplets is the sum of their areas, but if they coalesce, the final area is less than the area initially.
Conservation is not a general property of extensive quantities. In fact, most extensive quantities are not conserved (e.g., kinetic energy, potential energy, heat, work, the quantity $U+H$, ...). Conservation is generally stipulated by fundamental physical laws and even then there may be additional conditions. For example, energy is conserved only in non-relativistic systems.
Regarding dipole moments, the mean magnetic moment of $N$ spins in magnetic field $B_0$ is (see this reference)
$$M_0 = \frac{N(\gamma\bar h)^2 B_0}{4 k T}$$
and depends on temperature.This is the net macroscopic moment, i.e., the algebraic sum of all microscopic dipoles. The number of microscopic dipoles is conserved but the total moment, an extensive property, is not: it is zero at high temperatures (dipoles are randomly oriented) and increases as temperature is decreased (dipoles begin to align because they do not have enough energy to randomize).  If two systems under the same external field but different temperatures are mixed adiabatically the magnetic moment of the mixed state will be different from its value before mixing.
