Related papers: Statistical physics of the Schelling model of segr…
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…
Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
Many processes in nature seem to be entirely controlled by transition rates and the corresponding statistical dynamics. Some of them are in essence quantum, like the decay of excited states, the tunneling through barriers or the decay of…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
Ferrogels are smart soft materials, consisting of a polymeric network and embedded magnetic particles. Novel phenomena, such as the variation of the overall mechanical properties by external magnetic fields, emerge consequently. However,…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the…