Principle Of Least Dissipation Research Articles

Fluctuations and Irreversible Processes in Continuous Systems

A general derivation of the Onsager reciprocal relations for continuous thermodynamic systems is given in which the local fluxes of the extensive quantities enter directly. The fluctuation theory of Onsager and Machlup is extended to the derivation of a formula for the probability of the spontaneous occurrence in time of a distribution of local fluxes when the system is in equilibrium with a reservoir. There results a general principle of least dissipation for continuous thermodynamic systems.

Solution of the Stokes Flow of a Sphere by Minimization of the Dissipation of Energy

A detailed derivation of the velocity flow field of a sphere moving slowly through an incompressible viscous fluid of infinite extent (Stokes' flow) can be accomplished by simultaneously satisfying the equations of motion and continuity for the fluid particles. An alternate method is used here which makes use of Onsager's principle of least dissipation of energy. To simplify the problem a constant velocity U equal and opposite in direction to the velocity of the sphere is superposed on the system to allow the fluid to flow slowly in the +x direction past the now stationary sphere. A variational problem is then stated and a Euler-Lagrange equation is obtained, the solution of which specifies the velocity flow field dependence on r, the distance from the center of the sphere.

Fluctuations and Irreversible Processes

The probability of a given succession of (nonequilibrium) states of a spontaneously fluctuating thermodynamic system is calculated, on the assumption that the macroscopic variables defining a state are Gaussian random variables whose average behavior is given by the laws governing irreversible processes.This probability can be expressed in terms of the dissipation function; the resulting relation, which is an extension of Boltzmann's principle, shows the statistical significance of the dissipation function. From the form of the relation, the principle of least dissipation of energy becomes evident by inspection.