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In more technical language, a phase is a region in the [[parameter space]] of [[thermodynamics|thermodynamic variables]] in which the [[Thermodynamic free energy|free energy]] is [[analytic function|analytic]]; between such regions there are abrupt changes in the properties of the system, which correspond to discontinuities in the derivatives of the free energy function. As long as the free energy is analytic, all thermodynamic properties (such as [[entropy]], [[heat capacity]], [[magnetization]], and [[compressibility]]) will be [[well-behaved]], because they can be expressed in terms of the free energy and its [[derivative]]s. For example, the [[entropy]] is the negative of the first derivative of the free energy with [[temperature]] (at constant pressure).
 
Wann e Süßteem fon de ëijn Faaß en de annder övverjëijt, doh weed nommaal un_fö_jewööhnlej_en Schrett dohzwesche sėn, woh de fofööshbaare [[Ënnëjii (Füssėk)|Ënnëjii]] sesh nit annalüttėsch fo'hallde dëijt. Dad_eßss_enne [[FaaseÖvverjang]]. Wäje dämm dat dä Folouf_fon_de fofööshbaare Ënnëjii doh nit annalüttesch eß, wääde di op bëijde Sigge fom Övverjang dorsch zwëij ongerscheedlijje [[Funkzjohn (Mattemattik)|Funkzjohn]]e daajestëllt. Allsů de ëijn oddo anndere [[Tërrmodünaamėk|tërrmodünaamėsche Ëijeschaff]] weet sėsch noh dämm Övverjang annderß fohallde. Wat mer et miihßte en dämm Zosammehang belohre dëijd_eß de [[Wärmekappazėtäht]]. Jenou em Övverjang kann die [[on'ënndlesch]] wääde, oddo schlachaatėj_obb_enne anndere Wäät shprenge, oddo enne Kneck, dad_ess_en [[Onshteeteshkëijt (Mattemattik)||], en ier eetßte [[Afflëijdong (Mattemattik)||] han. Mieh doh drövver kam_me onger „[[Dünamėsche Dėfferenzkallorimetrii]]“ hohlësse.
When a system goes from one phase to another, there will generally be a stage where the free energy is non-analytic. This is a [[phase transition]]. Due to this non-analyticity, the free energies on either side of the transition are two different functions, so one or more thermodynamic properties will behave very differently after the transition. The property most commonly examined in this context is the [[heat capacity]]. During a transition, the heat capacity may become infinite, jump abruptly to a different value, or exhibit a "kink" or discontinuity in its [[derivative]]. See also [[differential scanning calorimetry]].
 
[[Image:Heat-capacity-transition.svg|thumb|400px|center|Mööschlejje Zosammehäng fun de Wärmemënge (C) met_e Temperatur (T) am Faase_Övverjang]]
Di Sigg heh stamp vun „https://ksh.wikipedia.org/wiki/Faaß_(Füsėk)“.