Related papers: Majorization and dynamics of continuous distributi…
The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (non-equilibrium) photon counting statistics in…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this…
We investigate the majorization order for comparing wave coherence and reveal its fundamental consequences in transport measurements, including power distribution, absorption, transmission, and reflection. We prove that all these…
Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and…
I propose to treat quantum evolution as a stochastic process consisting from a sequence of doubly stochastic matrices, which naturally arise in the generalized quantum evolution. Then it is proved that the law of non-decreasing entropy is…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been…
The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more…
Motivated by the idea of entanglement loss along Renormalization Group flows, analytical majorization relations are proven for the ground state of (1+1)-dimensional conformal field theories. For any of these theories, majorization is proven…
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and…
Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of…
Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer $n$ such that $\mu^{*n}$ is stochastically dominated by $\nu^{*n}$…
We explore the measurement problem in the entropic dynamics approach to quantum theory. The dual modes of quantum evolution---either continuous unitary evolution or abrupt wave function collapse during measurement---are unified by virtue of…
We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…
We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…