相关论文: Entropy rate calculations of algebraic measures
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of…
We consider statistical Markov Decision Processes where the decision maker is risk averse against model ambiguity. The latter is given by an unknown parameter which influences the transition law and the cost functions. Risk aversion is…
We study the baker's map and its Walsh quantization, as a toy model of a quantized chaotic system. We focus on localization properties of eigenstates, in the semiclassical regime. Simple counterexamples show that quantum unique ergodicity…
We obtain entropy formulas for SRB measures with finite entropy given by inducing schemes. In the first part of the work, we obtain Pesin entropy formula for the class of noninvertible systems whose SRB measures are given by Gibbs-Markov…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
We consider the problem of estimating the mean entropy production rate in a nonequilibrium process from the measurements of first-passage quantities associated with a single current. For first-passage processes with large thresholds, Refs.…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…
In this paper, the concept of L-algebra is revisited and after that, the article is prepared to deal with the notion of the entropy of an L-algebra. If a set has an L-algebraic structure, it is possible to calculate the degree of…
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
The irreversible currents and entropy production rate of a dilute colloidal suspension are calculated using the linear irreversible thermodynamics and the linear response theory. The \anomalous" or \hidden" entropy recently discussed in the…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…
Entropy production is arguably the most universally applicable measure of non-equilibrium behavior, particularly for systems coupled to a heat bath. This setting encompasses driven soft matter as well as biomolecular, biochemical, and…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…
In this paper we will give a short presentation of the quantum Levy-Khinchin formula and of the formulation of quantum continual measurements based on stochastic differential equations, matters which we had the pleasure to work on in…
We describe a quantum algorithm to estimate the $\alpha$-Renyi entropy of an unknown density matrix $\rho\in\mathcal{C}^{d\times d}$ for $\alpha\neq 1$ by combining the recent technique of quantum singular value transformations with the…