Intensity entropy generation

The entropy generated in a steady-state system is the entropy added to the surroundings, if this entropy is transported in a reversible manner. This is a convenient operational principle, because the surroundings can be idealized as composed of reservoirs, each with uniform intensive properties. 

Extended nonequilibrium thermodynamics is concerned with the nonlinear region and deriving the evolution equations with the dissipative flows as independent variables, besides the usual conserved variables. Typical nonequilib-rium variables such as flows and gradients of intensive properties may contribute to the rate of entropy generation. When the relaxation time of these variables differs from the observation time they act as constant parameters. The phenomenon becomes complex when the observation time and the relaxation time are of the same order, and the description of system requires additional variables. 

Mixing is an irreversible process, as the streams that are combined will generally have different temperatures. In the special case that the temperature of all inlet streams is the same (recall that all streams have the same pressure), then all streams, including the exit stream, have the same intensive properties and the entropy generation is zero. 

As in energy representation the fundamental thermodynamic equation in entropy representation (3) may also be subjected to Legendre transformation to generate a series of characteristic functions designated as Massieu-Planck (MP) functions, m. The index m denotes the number of intensive parameters introduced as independent variables, i.e. 

In essence, we wish to follow the Gibbs entropy maximization procedure of Section 5.2 backward in time. Specifically, we seek to characterize the final stage of equilibration when effective local equilibrium has been achieved in each small cell n, but cell intensities are not yet equalized throughout the system. To make direct contact with Section 5.2, we shall temporarily revert to the entropy representation (Section 5.3), which generates a scalar product and metric geometry that is conformally equivalent to the (/-based metric... 

Abstract. The Maximum Entropy method is a practical technique for generating intensity skymaps from Compton-telescope data. The application of the method to COMPTEL data for point sources and large-scale emission is described. New developments in the method are illustrated. 

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