Is there a rigorous definition of state of matter?

Question

Solid, liquid, and gas are all states of matter. However, I have never seen a rigorous definition of what a state of matter is. Is there such a definition somewhere? I would like to see such a definition.

Answer 1

You can go a long way with the following:

A plasma is an unbonded material whose fair fraction of constituents is ionized. (Implication: gaseous, strong electrical conductivity.)

Aside from that:

A gas is a material without a positive surface energy. (Implication: effortless spreading to fill a container. A bulk modulus similar to the pressure. Entropic bulk stiffness.)

Other than that:

A liquid is a material with a small shear modulus over the time scale of interest. (Implication: easy and rapid flow in response to a shear stress.)

A solid is the remaining material type in an association of four types—a relatively rigid connection of bonded constituents. (Implication: a notably large shear modulus. Enthalpic bulk stiffness.)

These are clearly not "rigorous"; Nature doesn't care how we classify what we observe and implement for various purposes. Nature presents the second law of thermodynamics: We tend to observe the configurations that are more likely to appear in the relevant context. A maximum of particle arrangements—that is, maximum entropy—is favorable, but strong bonding is also preferred because it tends to heat the rest of the universe, maximizing those particle arrangements. The interplay depends largely on the temperature, as temperature is the conjugate variable to entropy.

Practitioners in each area will undoubtedly wish to refine these definitions and their associated behavior.

Answer 2

The basic states of matter can be defined by the bulk properties of a substance. Does it fill its container ? Does it resist shear forces ? etc.

However, these basic states are a simplification which does not apply to all substances and in all conditions. For example, some substances have distinct mesophases which are intermediate between solid and liquid states. Other substances, such as ice, have many distinct solid phases with different properties.