English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present a proof of the monotonic entropy growth for a nonlineardiscrete-time model of a random market. This model, based on binary collisions,also may be viewed as a particular case of Ulam's redistribution of energyproblem. We represent each step of this dynamics as a combination of twoprocesses. The first one is a linear energy-conserving evolution of thetwo-particle distribution, 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 after the collision onevariable is integrated away. This coarse-graining is of the same type as thereal space renormalization group transformation and leads to an additionalentropy growth. The combination of these two factors produces the requiredresult which is obtained only by means of information theory inequalities.

Monotonic entropy growth for a nonlinear model of random exchanges