1211.2531 (S. M. Apenko)
S. M. Apenko
We present a proof of the monotonic entropy growth for a nonlinear discrete-time evolution which was proposed recently as a model of transactions between economical agents and which also represents a particular case of the Ulam's redistribution of energy problem. First we introduce an additional variable and consider a linear energy-conserving evolution on that extended space, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific coarse-graining of this linear evolution, when the additional variable is eliminated after the transformation. This coarse-graining is of the same type as in the real space renormalization group transformations and leads to an additional entropy growth. The combination of these two factors produce the required result which is obtained only by means of information theory inequalities.
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http://arxiv.org/abs/1211.2531
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