Onsager’s principle

Onsager s principle supplements these postulates and follows from the statistical theory of reversible fluctuations [5]. Onsager s principle states that when the forces and fluxes are chosen so that they are conjugate, the coupling coefficients are... 

In the simplest case, the reciprocation of two processes 1 and 2 is writ ten in accordance with the Onsager s principle as... 

Biot (1954) obtained the linear motion equation for n state variables qt in a closed system subject to generalized forces Q, and absolute temperature by introducing inner variables and applying Onsager s principle, given as follows ... 

We undertook a kinetic study of fluoride binding by HRP in collaboration with Robert Alberty while one of us (H.B.D.) was spending a sabbatical leave at the University of Wisconsin. The problem appeared to be simple and was ideally suited for the temperature-jump technique. Details of the kinetic results are pubhshed elsewhere (12, 13) but the simplest mechanism which is in accord with the kinetic data and does not violate Onsager s principle of detailed balancing 14) is... 

To derive an explicit form of the spectral dependence /(g, ui) (Equation 38), information on the correlation of density fluctuations in two different points at different instants of time is required. If the distance between these points and the wavelength is of the same order of magnitude, fluctuations must correlate in time, i.e. the density fluctuation at the first point at t = 0 may propagate or spread to the second point for time i. In this connection, the time correlation function can be derived in terms of the hydrodynamic equations and Onsager s principle. 

It seems that all the successfiilly elucidated dynamical imiversality classes adopt as their minimal models the ones described in terms of nonlinear Langevin equations (33). This indicates the general correctness of Onsager s principle as a fimdamental principle (beyond the linear regime). Just as equilibrium statistical mechanics is a statistical framework based on the principle (of equal... 

When a selected portion of a fluid exhibits a fluctuation, it is no longer in equilibrium with its surroundings. Consequently, the net thermodynamic force acting on a fluctuation is non-zero, and tends to drive the system back to equilibrium via the transport of mass and energy. The relaxation of fluctuations, occurs according to the macroscopic laws of hydrodynamics, with the macroscopic transport coefficients. This equality of macroscopic and mesoscopic relaxation is known as Onsager s principle. For example, in the absence of chemical reactions, the hydrodynamic equation expressing the conservation of concentration c in a binary fluid is... 

The original Onsager s principle of last dissipation of energy is derivable by the presentation of the force potential with the minimum task (38) of Legendre s transform. Namely, using the definition (38) which was actualized on vector -processes, we get ... 

Due to the Onsager s principle of last dissipation of energy this functional is maximal with respect to variations of the fluxes j,. The necessary condition of the maximum are the constitutive equations, which are presented as Euler-Lagrange equations ... 

Ziegler H (1963) An attemp to generalize Onsager s principle, and its significance for... 

By Onsager s principle brq = bqr and in view of the dissipation inequality (6.8), b>0 and brq are components of a semipositive definite, symmetric matrix. As noted earlier, the times r and t in (6.12) and (6.13) are distinct because the quench time t usually occurs earlier than the exposure time t, namely t = z — t. ... 

Some of the variational principles which are to be described in the present article, are very closely connected with Onsager s reciprocity relationsAlthough there have been various methods of derivation of this theorem, we shall follow the traditional method of derivation by Onsager and Casimir. This is based on the consideration of fluctuations in an aged system, and this method is also connected with the derivation of Onsager s principle of least dissipation of energy. ... 

We must be extremely careful about the condition under which we maximize the left-hand side of Eq. 54. In Onsager s principle of least dissipation of energy, the forces are fixed at... 

As seen in the above k tp, f has certain features analogous to the dissipation function, but there are essential differences between these two functions. The brace ip, ip], contains no empirical transport coefficients but depends only on the inter-molecular forces, whereas the dissipation function is a quadratic form with the empirical transport coefficients as its coefficients. Then in the case of Eq. 84, the variational principle leads to the maximum values of the transport coefficients compatible with the restrictions. This is the principle of maximum transport coefficients stated in Nakai s paper on the kinetic theory of gases. On the other hand, Onsager s principle of least dissipation of energy is merely a mathematical reformulation of the linear relations and hence is independent of the magnitude of these coefficients. 

It has been shown by Mazur and Overbeek that the validity of this relation is of a very general character and a direct consequence of Onsager s principle of reciprocity of irreversible phenomena ... 

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