Related papers: Path collective variables without paths
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
We develop a new fermionic path-integral formalism to analyze the phase diagram of open nonequilibrium systems. The formalism is applied to analyze an ensemble of two-level atoms interacting with a single-mode optical cavity, described by…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the…
Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…
When examining dynamics occurring at non-zero temperatures, both energy and entropy must be taken into account while describing activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe…
Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of…
Virtual states are a central concept in quantum mechanics. By definition, the probability of finding a quantum system in a virtual state should be vanishingly small at all times. In contrast to this notion, we report a phenomenon occurring…
Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within…
The problem of computing the rate of diffusion-aided activated barrier crossings between metastable states is one of broad relevance in physical sciences. The transition path formalism aims to compute the rate of these events by analysing…
Molecular dynamics (MD) simulations are useful in obtaining thermodynamic and kinetic properties of bio-molecules but are limited by the timescale barrier, i.e., we may be unable to efficiently obtain properties because we need to run…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and…
This paper extends our earlier studies of free energy functions of density and crystalline order parameters for models of supercooled water, which allows us to examine the possibility of two distinct metastable liquid phases [J. Chem. Phys.…
We study the dynamical behavior of a one dimensional interface interacting with a sticky unpenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contact between the interface and the substrate…
The semiclassical Euclidean path integral method is applied to compute the low temperature quantum decay rate for a particle placed in the metastable minimum of a cubic potential in a {\it finite} time theory. The classical path, which…
We describe a simple model of heterogeneous, interacting agents making decisions between $n\ge 2$ discrete choices. For a special class of interactions, our model is the mean field description of random-field Potts-like models, and is…