Related papers: Information thermodynamics of transition paths bet…
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…
We study the trajectories of a solution $X_t$ to an It\^o stochastic differential equation in $\Rm^d$, as the process passes between two disjoint open sets, $A$ and $B$. These segments of the trajectory are called transition paths or…
A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation…
The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results…
Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent…
Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a…
Two quantum systems, each described as a random-matrix ensemble. are coupled to each other via a number of transition states. Each system is strongly coupled to a large number of channels. The average transmission probability is the product…
In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical…
Many dynamical systems consist of multiple, co-evolving subsystems (degrees of freedom). These subsystems often depend upon each other in a way that restricts the overall system's dynamics. How does this network of dependencies affect the…
We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how…
Nascent quantum computers motivate the exploration of quantum many-body systems in nontraditional scenarios. For example, it has become natural to explore the dynamics of systems evolving under both unitary evolution and measurement. Such…
The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific…
A consistent description of simultaneous heat and particle transport, including cross effects, and the associated entropy balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where,…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed…
The information implicitly represented in the state of physical systems allows one to analyze them with analytical techniques from statistical mechanics and information theory. In the case of complex networks such techniques are inspired by…
A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic…
Rare transitions between long-lived stable states are often analyzed in terms of free energy landscapes computed as functions of a few collective variables. Here, using transitions between geometric phases as example, we demonstrate that…