In its liquid form, water also displays negative thermal expansivity below 3.984 C.

The expansivity of the components of the mixture can cancel each other like in invar.

The thermal expansivity is defined as:

Positive expansivity is much stronger than expansivity.

In an isobaric process, the volumetric thermal expansivity, which we denote , is given by the ideal gas law:

In mathematics, the notion of expansivity formalizes the notion of points moving away from one another under the action of an iterated function.

However, the glass transition may be described as analogous to a second-order phase transition where the intensive thermodynamic variables such as the thermal expansivity and heat capacity are discontinuous.

A complex behavior of the doping element (quantified in terms of some parameters ( Urbach energy, Vickers hardness, optothermal expansivity, Faraday effect , band gap.)

The idea of expansivity is fairly rigid, as the definition of positive expansivity, below, as well as the Schwarz-Ahlfors-Pick theorem demonstrate.

The differences in expansivity can be accounted for if the interaction parameter is now expressed as where the first term reflects the interchange energy on forming contacts of unlike type and includes segment size differences, while the second term is the new 'structural' contribution coming from free volume changes on mixing a dense polymer with an expanded solvent.

The space is often assumed to be compact, since under that assumption expansivity is a topological property; i.e. if is any other metric generating the same topology as , and if is expansive in , then is expansive in (possibly with a different expansivity constant).