We show how to compute the probability distributions of the order parameter of the O(n) model at two-loop order of perturbation theory generalizing the methods developed for computing the same in case of the Ising model (Sahu 2025 J. Stat. Mech. 2025 123202). We show that even for the O(n) model, there exists not one but a family of these probability distribution functions (PDFs) indexed by ζ which is the ratio of system size L to the bulk correlation length ξ∞. We also compare these PDFs to the Monte-Carlo simulations and the existing FRG results (Rançon et al 2025 arXiv:2501.04465 [cond-mat.statmech]) for the O(2) and O(3) models.
Understanding the transport of particles immersed in a carrier fluid (bedload transport) is still an exciting challenge. Among the different types of gas-solid flows, when the dynamics of solid particles is essentially dominated by collisions between them, kinetic theory can be considered as a reliable tool to derive continuum approaches from a fundamental point of view. In a recent paper, Chassagne et al. [J. Fluid Mech. 964, A27, (2023)] have proposed a two-fluid model based on modifications to a classical kinetic theory model. First, in contrast to the classical model, the model proposed by Chassagne et al. (2023) takes into account the interparticle friction not only in the radial distribution function but also through an effective restitution coefficient in the rate of dissipation term of granular temperature. As a second modification, at the top of the bed where the volume fraction is quite small, the model accounts for the saltation regime in the continuum framework. The theoretical results derived from the model agree with discrete simulations for moderate and high densities and they are also consistent with experiments. Thus, the model proposed by Chassagne et al. (2023) helps to a better understanding on the combined impact of friction and inelasticity on the macroscopic properties of granular flows.
We present technical results required for the description and understanding of correlations and fluctuations of the empirical density and current as well as diverse time-integrated and time-averaged thermodynamic currents of diffusion processes with a general time dependence on all time scales. In particular, we generalize the results from Dieball and Godec (2022 Phys. Rev. Lett. 129 140601); Dieball and Godec (2022 Phys. Rev. Res. 4 033243); Dieball and Godec (2022 arXiv:2206.04034 [cond-mat.stat-mech]) to additive functionals with explicit time dependence and transient or non-ergodic overdamped diffusion. As an illustration we apply the results to two-dimensional harmonically confined overdamped diffusion in a rotational flow evolving from a non-stationary initial distribution.
Abstract We introduce a minimalist dynamical model of wealth evolution and wealth sharing among N agents as a platform to compare the relative merits of altruism and individualism. In our model, the wealth of each agent independently evolves by diffusion. For a population of altruists, whenever any agent reaches zero wealth (that is, the agent goes bankrupt), the remaining wealth of the other N − 1 agents is equally shared among all. The population is collectively defined to be bankrupt when its total wealth falls below a specified small threshold value. For individualists, each time an agent goes bankrupt (s)he is considered to be ‘dead’ and no wealth redistribution occurs. We determine the evolution of wealth in these two societies. Altruism leads to more global median wealth at early times; eventually, however, the longest-lived individualists accumulate most of the wealth and are richer and more long lived than the altruists.
Since Hasselmann and Leith, stochastic Energy Balance Models (EBMs) have allowed treatment of climate fluctuations, and at least the possibility of fluctuation-dissipation relations.   However, it has recently been argued that observations motivate heavy-tailed temporal response functions in global mean temperature. Our complementary approach  (arXiv:2007.06464v2[cond-mat.stat-mech]) exploits the correspondence  between Hasselmann’s EBM and  Langevin’s equation (1908).  We propose mapping the Mori-Kubo Generalised Langevin Equation (GLE) to generalise the Hasselmann EBM. If present, long range memory then simplifies the GLE to a fractional Langevin equation (FLE).  We describe the EBMs that correspond to the GLE and FLE,  and relate them to  Lovejoy et al’s FEBE [NPG Discussions, 2019; QJRMS, to appear, 2021].
We use the cellular automaton (CA) approach to model binary diffusion in solids. We define an asynchronous CA model and formally take its continuum limit and show it approaches a differential equation model derived in previous work (Ribera, Wetton, and Myers, 2019, arXiv:1911.07359 [cond-mat.stat-mech]) that exhibits the Kirkendall effect. The framework allows the exploration of other state change rules based on additional physical mechanisms.