1. A method of determining uniquely underlying sources forming a source vector S&equals;(S 1, S 2,... ) propagating through a nonlinear mixing medium of a constant temperature, open equilibrium system by measuring multiple radiation components forming a data vector per single pixel X&equals;(X 1, X 2,... ), comprising: measuring the data vector X; applying a constraint to the equilibrium system such that the thermal diffusion of the equilibrium system is constrained isothermally at the equilibrium free energy, wherein the equilibrium free energy is the Helmholtz free energy H&equals;E−TS, wherein E is the energy, T is the equilibrium reservoir temperature, and S is the classical Shannon information theory entropy; defining a state of the open equilibrium system by a feed-forward first order error energy E(X/S)&equals;&mgr;&lcub;g(&lsqb;W&rsqb;X)−S), wherein g is the Lagrange constraint vector and &lsqb;W&rsqb; is the feed-foward matrix; reducing the feed-forward first order energy E(X/S) to a second order Least Mean Square (LMS) error energy for a specific Lagrange constraint vector &mgr;; and determining from among all possible vector sources S&equals;(S 1, S 2,... ) the one vector source that satisfies the minimum H for an arbitrary mixing matrix &lsqb;A&rsqb; and smooth nonlinearity g: X&equals;g −1 &lcub;&lsqb;A&rsqb;S&rcub;, wherein &lsqb;A&rsqb; is the heat transport mixing matrix and is the inverse of &lsqb;W&rsqb;.