Characteristic state function

Characteristic state function

The characteristic state function in statistical mechanics refers to a particular relationship between the partition function of an ensemble.

In particular, if the partition function P satisfies

P = exp( − βQ) or P = exp( + βQ)

in which Q is a thermodynamic quantity, then Q is known as the "characteristic state function" of the ensemble corresponding to "P". Beta refers to the thermodynamic beta.

Examples

• The microcanonical ensemble satisfies $\Omega(U,V,N) = e^{ \beta T S} \;\,$ hence, its characteristic state function is $TS \;\, .$ This quantity roughly speaking, denotes the energy of the entropy at a particular temperature.
• The canonical ensemble satisfies $Z(T,V,N) = e^{- \beta A} \,\;$ hence, its characteristic state function is the Helmholtz free energy.
• The grand canonical ensemble satisfies $\Xi(T,V,\mu) = e^{\beta P V} \,\;$, so its characteristic state function is the total Pressure-volume work.
• The isothermal-isobaric ensemble satisfies $\Delta(N,T,P) = e^{-\beta G} \;\,$ so its characteristic function is the Gibbs free energy.

Wikimedia Foundation. 2010.

Look at other dictionaries:

• Characteristic function — In mathematics, characteristic function can refer to any of several distinct concepts: The most common and universal usage is as a synonym for indicator function, that is the function which for every subset A of X, has value 1 at points of A and… …   Wikipedia

• State space (controls) — In control engineering, a state space representation is a mathematical model of a physical system as a set of input, output and state variables related by first order differential equations. To abstract from the number of inputs, outputs and… …   Wikipedia

• State machine replication — Introduction from Schneider s 1990 survey: : Distributed software is often structured in terms of clients and services. Each service comprises one or more servers and exports operations that clients invoke by making requests. Although using a… …   Wikipedia

• Partition function (statistical mechanics) — For other uses, see Partition function (disambiguation). Partition function describe the statistical properties of a system in thermodynamic equilibrium. It is a function of temperature and other parameters, such as the volume enclosing a gas.… …   Wikipedia

• Schwinger function — In quantum field theory, the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to the ordered set of points in Euclidean space with no coinciding points. These functions are… …   Wikipedia

• Wave function — Not to be confused with the related concept of the Wave equation Some trajectories of a harmonic oscillator (a ball attached to a spring) in classical mechanics (A B) and quantum mechanics (C H). In quantum mechanics (C H), the ball has a wave… …   Wikipedia

• Wave function collapse — Quantum mechanics Uncertainty principle …   Wikipedia

• Postictal state — Symptoms= Jerome Engel defines the postictal state as “manifestations of seizure induced reversible alterations in neuronal function but not structure.” cite book last = Engel first = Jerome Jr. authorlink = Engel title = Seizures and Epilepsy… …   Wikipedia

• Full state feedback — (FSF), or pole placement, is a method employed in feedback control system theory to place the closed loop poles of a plant in pre determined locations in the s plane. Placing poles is desirable because the location of the poles corresponds… …   Wikipedia

• Control-Lyapunov function — In control theory, a control Lyapunov function V(x,u) [1]is a generalization of the notion of Lyapunov function V(x) used in stability analysis. The ordinary Lyapunov function is used to test whether a dynamical system is stable (more… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”