Related papers: Augmented Transition Path Theory for Sequences of …
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a…
Interaction networks, consisting of agents linked by their interactions, are ubiquitous across many disciplines of modern science. Many methods of analysis of interaction networks have been proposed, mainly concentrating on node degree…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
The ability to model continuous change in Reiter's temporal situation calculus action theories has attracted a lot of interest. In this paper, we propose a new development of his approach, which is directly inspired by hybrid systems in…
It is considered to re-formulate quantum theory as it appears: A theory of continuous and causal time evolution, interrupted by discontinuous and stochastic jumps. To develop the (missing) theory of jumps a heuristic-phenomenological…
Quantifying animal interactions is crucial for understanding various ecological processes, including social community structures, predator-prey dynamics, spreading of pathogens and information. Despite the ubiquity of interaction processes…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
A central concern across the natural sciences is a quantitative understanding of the mechanism governing rare transitions between two metastable states. Recent research has uncovered a fundamental equality between the time-reversal…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
A rigorous theory of liquid-crystal transitions is developed starting from the Liouville equation. The starting point is an all-atom description and a set of order parameter field variables that are shown to evolve slowly via Newton's…
The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat…
The concept of reaction extent (the progress of a reaction, advancement of the reaction, conversion, etc.) was introduced around 100 years ago. Most of the literature provides a definition for the exceptional case of a single reaction step…
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
Stochastic processes play a key role for modeling a huge variety of transport problems out of equilibrium, with manifold applications throughout the natural and social sciences. To formulate models of stochastic dynamics the conventional…
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation…
The modern theory of rare events is grounded in near equilibrium ideas, however many systems of modern interest are sufficiently far from equilibrium that traditional approaches do not apply. Using the recently developed variational path…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…