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thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
, Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol \Psi (Psi), is defined by the following relation: : \Psi = \Psi \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, where for every
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expresse ...
with degree of freedom ''r'' one may choose r variables, e.g. \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, , to define a coordinate system, where ''X'' and ''Y'' are extensive and
intensive In grammar, an intensive word form is one which denotes stronger, more forceful, or more concentrated action relative to the root on which the intensive is built. Intensives are usually lexical formations, but there may be a regular process for for ...
variables, respectively, and where at least one extensive variable must be within this set in order to define the size of the system. The (''r'' + 1)-th variable, \Psi , is then called the Massieu function.Inden, Gerhard. (2008). �
Introduction to Thermodynamics
��, ''Materials Issues for Generation IV Systems'', pgs. 73–112. Springer
The Massieu function was introduced in the 1869 paper "On the Characteristic Functions of Various Fluids" by French engineer François Massieu (1832-1896). The name "Gibbs function" is the eponym of American physicist Willard Gibbs (1839-1903), who cited Massieu in his 1876 '' On the Equilibrium of Heterogeneous Substances''. Massieu, as discussed in the first footnote to the abstract of Gibbs' ''Equilibrium'', “appears to have been the first to solve the problem of representing all the properties of a body of invariable composition which are concerned in reversible processes by means of a single function.” Massieu's 1869 paper seems to be the source for the generalized mathematical conception of the
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of h ...
of a system being equal to summations of the products of pairs of
conjugate variables Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation� ...
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References


Further reading

*{{cite journal , last1=Massieu , first1=F. , title=Sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs , journal=Comptes rendus , date=1869 , volume=69 , pages=858–862 , url=https://babel.hathitrust.org/cgi/pt?id=uc1.31822009518986&view=1up&seq=864 , trans-title=On the characteristic functions of various fluids and on the theory of vapors , language=French *Massieu, François. (1876). ''Thermodynamique : Mémoire sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs''. 92 pgs. Académie des Sciences de L'Institut National de France. Thermodynamics