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Employing molecular dynamics simulations of jammed soft particles, we studymicroscopic responses of force-chain networks to quasi-static isotropic(de)compressions. We show that not only contacts but also interparticle gapsbetween the nearest neighbors must be considered for the stochastic evolutionof the probability distribution functions (PDFs) of forces, where the mutualexchange of contacts and interparticle gaps, i.e. opening and closing contacts,are also crucial to the incremental system behaviors. By numericallydetermining the transition rates for all changes of contacts and gaps, weformulate a Master equation for the PDFs of forces, where the insight one getsfrom the transition rates is striking: The mean change of forces reflectsnon-affine system response, while their fluctuations obey uncorrelated Gaussianstatistics. In contrast, interparticle gaps are reacting mostly affine inaverage, but imply multi-scale correlations according to a wider stabledistribution function.

Master equation for the probability distribution functions of forces in soft particle packings