A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random numbers of particles in cells of given position and...

The representation of the economic system, from a complexity perspective, focuses on interactions among heterogeneous agents in conditions of uncertainty. Heterogeneity entails asymmetric reactions to shocks and, through interaction mechanisms and feedback loops at micro, macro and meso level,...