Related papers: On the abrupt change of the maximum likelihood sta…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We investigate a simple model corresponding to particles driven in opposite directions and interacting via a repulsive potential. The particles move off-lattice on a periodic strip and are subject to random forces as well. We show that this…
We demonstrate that turbulent zonal jets, analogous to Jovian ones, which are quasi-stationary, are actually metastable. After extremely long times, they randomly switch to new configurations with a different number of jets. The genericity…
We consider simple stochastic climate models, described by slowly time-dependent Langevin equations. We show that when the noise intensity is not too large, these systems can spend substantial amounts of time in metastable equilibrium,…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
The Earth is well-known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realised. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a…
We consider a stochastic $N$-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we show that the propagation of chaos does…
Stochastic thermodynamics is the field of study relating fluctuations in stochastic systems to thermodynamic quantities. The total entropy production (EP), is central to the thermodynamic classification of systems. Non-equilibrium systems…
Tetrahedral liquids such as water and silica-melt show unusual thermodynamic behavior such as a density maximum and an increase in specific-heat when cooled to low temperatures. There is a debate in the literature whether these phenomena…
We study a zero-range process with system-size dependent jump rates, which is known to exhibit a discontinuous condensation transition. Metastable homogeneous phases and condensed phases coexist in extended phase regions around the…
When we lower the temperature of a liquid, at some point we meet a first order phase transition to the crystal. Yet, under certain conditions it is possible to keep the system in its metastable phase and to avoid crystallization. In this…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward…
Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero.…
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
Whether the glass transition is caused by an underlying singularity or is a purely kinetic phenomenon is a significant outstanding question. Studying an atomistic glass former, we introduce a sampling method to access temperatures…
The evolution and sudden change of steady interaction structures is numerically studied with the fore wedge angle theta_1 in a low enthalpy hypersonic double wedge configuration. It particularly focuses on the conditions of Swantek and…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…