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An invariant state of a quantum Markov semigroup is an equilibrium state if it satisfies a quantum detailed balance condition. In this paper, we introduce a notion of entropy production for faithful normal invariant states of a quantum…
We study the scaling of the entanglement entropy in different classes of one-dimensional fermionic quasiperiodic systems with and without pairing, focusing on multifractal critical points/phases. We find that the entanglement entropy scales…
In this paper we calculate Kolmogorov-Sinai entropy $h_M(S)$ of the generalized Markov shift associated with a contractive Markov system (CMS) \cite{Wer1} using the coding map constructed in \cite{Wer3}. We show that…
We discuss a class of coupled systems of nonlocal nonlinear balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution are proven via…
We develop the a posteriori error analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under…
Non-classical resources enable measurements to achieve a precision that exceeds the limits predicted by the central limit theorem. However, environmental noise arising from system-environment interactions severely limits the performance of…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
We investigate logarithmic corrections to the entropy of supersymmetric, rotating, asymptotically AdS$_5$ black holes and black strings. Within the framework of the AdS/CFT correspondence, the entropy of these black objects is determined,…
Relative entropy measure quantifying coherence, a key property of quantum system, is proposed recently. In this note, we investigate the maximally coherent state (MCS) with respect to relative entropy measure. %(denoted by $\mathcal…
We study finite-time spectral rigidity in reversible Markov chains via exact spectral relaxation dynamics. While the underlying identities follow classically from self-adjointness on $L^2(\pi)$, organizing the dynamics around the relaxation…
I present an approach to calculate the finite-frequency quantum noise in systems strongly coupled to structured reservoirs based on the Markovian embedding. This technique consists of mapping of the non-Markovian dynamics of the original…
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are…
We formalize the derivation of a generalized coarse-graining $n$-resolved master equation by introducing a virtual detector counting the number of transferred charges in single-electron transport. Our approach enables the convenient…
We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be…
The brick wall model is a semi-classical approach to understanding the microscopic origin of black hole entropy. We outline the formalism for the brick wall model in arbitrary number of dimensions and generalize it to include both charged…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
We study the non-equilibrium dynamics of a one-dimensional system of hard core bosons (HCBs) in the presence of an onsite potential (with an alternating sign between the odd and even sites) which shows a quantum phase transition (QPT) from…
We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the…
We investigate the existence and properties of kink-like solitons in a class of models with two interacting scalar fields. In particular, we focus on models that display both double and single-kink solutions, treatable analytically using…
We present a general method for calculating R\'enyi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends. In the conformal field theory framework, this…