The Second Law of Economics by Reiner Kümmel

Author:Reiner Kümmel
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(3.17)

This most general formulation of the second law of thermodynamics can be made more explicit for a nonequilibrium system that contains N different sorts of particles k, which do not undergo chemical reactions.12 If thermodynamic variables such as temperature and pressure remain well defined locally during all changes, nonequilibrium thermodynamics [51] yields the density of (dissipative) entropy production (σ S, dis) as

(3.18)

The gradient operator ∇ represents the vectorial sum of spatial derivatives, which operate on the absolute temperature T and the chemical potentials μ k of the particles of type k. The gradients of temperature and chemical potentials, and specific external forces f k , which act on the particles, represent the generalized forces that drive the heat current density j Q and the diffusion current densities j k . At each point all diffusion current densities cancel, so total mass is conserved everywhere:

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