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While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…

Statistics Theory · Mathematics 2007-07-16 Peter Gacs , John Tromp , Paul Vitanyi

In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of…

Quantum Physics · Physics 2007-07-16 Fabio Benatti , Tyll Krueger , Markus Mueller , Rainer Siegmund-Schultze , Arleta Szkola

We theoretically investigate how information flows when two particles interact with each other. Understanding the physical mechanisms of directional information flow is crucial for advancing information thermodynamics and stochastic…

Statistical Mechanics · Physics 2026-03-12 Tenta Tani

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…

Statistical Mechanics · Physics 2014-05-28 Scott Aaronson , Sean M. Carroll , Lauren Ouellette

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

Computational Complexity · Computer Science 2007-05-23 Paul Vitanyi

The study of noise assisted transport in quantum systems is essential in a wide range of applications from near-term NISQ devices to models for quantum biology. Here, we study a generalised XXZ model in the presence of stochastic collision…

Quantum Physics · Physics 2023-11-16 Alessandro Civolani , Vittoria Stanzione , Maria Luisa Chiofalo , Jorge Yago Malo

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…

chao-dyn · Physics 2013-01-16 Valentin V. Sokolov , B. Alex Brown , Vladimir Zelevinsky

In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the…

Quantum Physics · Physics 2007-05-23 Andre Berthiaume , Wim van Dam , Sophie Laplante

In this article, the dynamics and complexity of a noise induced blood flow system have been investigated. Changes in the dynamics have been recognized by measuring the periodicity over significant parameters. Chaotic as well as non-chaotic…

Adaptation and Self-Organizing Systems · Physics 2020-01-08 Bo Yan , Sayan Mukherjee , Shaobo He

In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vitanyi has been examined. In the quantum information theory, the information-disturbance relationship,…

Quantum Physics · Physics 2011-05-16 Takayuki Miyadera

Kolmogorov argued that the concept of information exists also in problems with no underlying stochastic model (as Shannon's information representation) for instance, the information contained in an algorithm or in the genome. He introduced…

Discrete Mathematics · Computer Science 2008-07-01 Joel Ratsaby

Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…

Information Theory · Computer Science 2020-07-15 Hector Zenil

Research into active networking has provided the incentive to re-visit what has traditionally been classified as distinct properties and characteristics of information transfer such as protocol versus service; at a more fundamental level…

Computational Complexity · Computer Science 2016-11-17 Stephen F. Bush

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…

Quantum Physics · Physics 2025-01-22 Michał Oszmaniec , Marcin Kotowski , Michał Horodecki , Nicholas Hunter-Jones

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as…

Information Theory · Computer Science 2011-11-29 David Balduzzi

The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…

Computational Complexity · Computer Science 2016-05-06 Anatol Slissenko

Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…

Information Theory · Computer Science 2015-04-21 Alexander Shen

A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…

Data Analysis, Statistics and Probability · Physics 2013-01-18 Eugene Perevalov , David Grace

The information processing capacity of a complex dynamical system is reflected in the partitioning of its state space into disjoint basins of attraction, with state trajectories in each basin flowing towards their corresponding attractor.…

Disordered Systems and Neural Networks · Physics 2007-05-23 Peter Krawitz , Ilya Shmulevich

Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…

Quantum Physics · Physics 2024-11-07 Jason Pollack , Dylan VanAllen