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For a refracted L\'evy process driven by a spectrally negative L\'evy process, we use a different approach to derive expressions for its q-potential measures without killing. Unlike previous methods whose derivations depend on scale…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much beyond the original cascade construction of Mandelbrot. We…
Irreversibility is a fundamental concept with important implications at many levels. It pinpoints the fundamental difference between the intrinsically reversible microscopic equations of motion and the unidirectional arrow of time that…
We introduce and compare several measures of nonclassical correlation defined on the basis of a widely-recognized paradigm claiming that a multipartite system represented by a density matrix having no product eigenbasis possesses…
The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to…
In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost…
We derive a geometrical expression of the excess entropy production for quasi-static transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The…
This paper focuses on the estimation of partially observed branching processes. First, the estimators from a frequentist perspective proposed in the literature are reviewed. The main objective of this paper is to present computational tools…
We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the…
We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
First, using the method of the soliton-solution, the fermion probability density equation, which corresponds to the Dirac equation, is derived. Next, we extend the chaos theory, in which the period bifurcation is equivalent to the particle…
Amplitude- and truncated partial-wave analyses are combined into a single procedure and a novel, almost theory-independent single-channel method for extracting multipoles directly from measured data is developed. In practice, we have…
We argue that specific fluctuations observed in high-energy nuclear collisions can be attributed to intrinsic fluctuations of temperature of the hadronizing system formed in such processes and therefore can be described by the same…
A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…
We consider the process gamma^* N -> M_1 M_2 N' with a large rapidity gap between the two mesons M_1 and M_2. Within the QCD collinear approximation, the scattering amplitude may be written as a convolution of an impact factor describing…
Entropy production and the detailed fluctuation theorem are of fundamental importance for thermodynamic processes. In this paper, we study the multiple entropy production for multitime quantum processes in a unified framework. For closed…
Threshold amplitudes are considered for $n$-particle production in arbitrary scalar theory. It is found that, like in $\phi ^4$, leading-$n$ corrections to the tree level amplitudes, being summed over all loops, exponentiate. This result…
The extended Gaussian ensemble introduced recently as a generalization of the canonical ensemble, which allows to treat energy fluctuations present in the system, is used to analyze the inelasticity distributions in high energy…