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We extend the theory of labeled Markov processes with internal nondeterminism, a fundamental concept for the further development of a process theory with abstraction on nondeterministic continuous probabilistic systems. We define…

Logic in Computer Science · Computer Science 2015-03-17 Pedro D'Argenio , Pedro Sánchez Terraf , Nicolás Wolovick

In the general process of eliminating dynamic variables in Markovian models, there exists a difference in the irreversible entropy production between the original and reduced dynamics. We call this difference the hidden entropy production,…

Statistical Mechanics · Physics 2022-06-28 Kyogo Kawaguchi , Yohei Nakayama

This paper considers the speed of convergence (mixing) of a finite Markov kernel $P$ with respect to the Kullback-Leibler divergence (entropy). Given a Markov kernel one defines either a discrete-time Markov chain (with the $n$-step…

Probability · Mathematics 2024-09-13 Pietro Caputo , Zongchen Chen , Yuzhou Gu , Yury Polyanskiy

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…

Optimization and Control · Mathematics 2022-09-13 Michelle S. Chong

In this paper we study the notion of estimation entropy recently established by Liberzon and Mitra. This quantity measures the smallest rate of information about the state of a dynamical system above which an exponential state estimation…

Dynamical Systems · Mathematics 2017-05-08 Christoph Kawan

Entropy production (EP) is known as a fundamental quantity for measuring the irreversibility of processes in thermal equilibrium and states far from equilibrium. In stochastic thermodynamics, the EP becomes more visible in terms of the…

Statistical Mechanics · Physics 2020-06-24 Jaewoo Jung , Jaegon Um , Deokjae Lee , Yong W. Kim , D. Y. Lee , H. K. Pak , B. Kahng

In this work we present results about the rate of (relative) information loss induced by passing a real-valued, stationary stochastic process through a memoryless system. We show that for a special class of systems the information loss rate…

Information Theory · Computer Science 2013-04-19 Bernhard C. Geiger , Gernot Kubin

In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without…

Probability · Mathematics 2016-08-09 Alonso-Ruiz , Spodarev

We present rigorous results on some open questions on NSRPS, non sequential recursive pairs substitution method (see Grassberger in \cite{G}). In particular, starting from the action of NSRPS on finite strings we define a corresponding…

Statistical Mechanics · Physics 2009-11-11 Dario Benedetto , Emanuele Caglioti , Davide Gabrielli

Consider a measure-preserving transition kernel $T$ on an arbitrary probability space $(\mathbb X,\mathcal cA,\pi)$. In this level of generality, we prove that a one-step hyper-contractivity estimate of the form $\|T\|_{p\to q}\le 1$ with…

Probability · Mathematics 2026-02-20 Justin Salez

In this paper, we continue the investigation of quantum Markov states (QMS) and define their mean entropies. Such entropies are explicitly computed under certain conditions. The present work takes a huge leap forward at tackling one of the…

Mathematical Physics · Physics 2022-09-28 Farrukh Mukhamedov , Abdessatar Souissi

We estimate the distance in total variation between the law of a finite state Markov process at time t, starting from a given initial measure, and its unique invariant measure. We derive upper bounds for the time to reach the equilibrium.…

Probability · Mathematics 2015-06-26 Pierre MATHIEU , Pierre PICCO

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

Data Analysis, Statistics and Probability · Physics 2016-01-05 Elliot A. Martin , Jaroslav Hlinka , Alexander Meinke , Filip Děchtěrenko , Jörn Davidsen

We consider a general piecewise deterministic Markov process (PDMP) $X=\{X_t\}_{t\geqslant 0}$ with measure-valued generator $\mathcal{A}$, for which the conditional distribution function of the inter-occurrence time is not necessarily…

Probability · Mathematics 2017-04-27 Zhaoyang Liu , Yuying Liu , Guoxin Liu

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of…

Optimization and Control · Mathematics 2021-05-18 Yagiz Savas , Michael Hibbard , Bo Wu , Takashi Tanaka , Ufuk Topcu

We consider the task of deriving a key with high HILL entropy from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was $\eps$ indistinguishable from having min-entropy was via…

Cryptography and Security · Computer Science 2015-04-29 Maciej Skorski , Alexander Golovnev , Krzysztof Pietrzak

In [Haruna, T. and Nakajima, K., 2011. Physica D 240, 1370-1377], the authors introduced the duality between values (words) and orderings (permutations) as a basis to discuss the relationship between information theoretic measures for…

Chaotic Dynamics · Physics 2015-06-04 Taichi Haruna , Kohei Nakajima

In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…

Quantum Physics · Physics 2024-12-18 Benjamin Schumacher , Michael D. Westmoreland

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

Statistics Theory · Mathematics 2016-06-29 Gordon V. Chavez , Richard Kleeman

We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility…

Mathematical Physics · Physics 2017-08-02 Tristan Benoist , Vojkan Jaksic , Yan Pautrat , Claude-Alain Pillet