DOI: 10.3390/e18120426

# On Macrostates In Complex Multi-Scale Systems

Harald Atmanspacher

Published 2016 · Mathematics, Computer Science

A characteristic feature of complex systems is their deep structure, meaning that the definition of their states and observables depends on the level, or the scale, at which the system is considered. This scale dependence is reflected in the distinction of micro- and macro-states, referring to lower and higher levels of description. There are several conceptual and formal frameworks to address the relation between them. Here, we focus on an approach in which macrostates are contextually emergent from (rather than fully reducible to) microstates and can be constructed by contextual partitions of the space of microstates. We discuss criteria for the stability of such partitions, in particular under the microstate dynamics, and outline some examples. Finally, we address the question of how macrostates arising from stable partitions can be identified as relevant or meaningful.

This paper references

10.1109/PHYCMP.1992.615556

Information In Dynamics

N. Gershenfeld (1992)

10.1007/978-1-4684-8771-8_14

Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems

H. Primas (1990)

10.1016/0375-9601(93)90232-O

Measuring complexity using information fluctuation

J. E. Bates (1993)

Autopoiesis and Cognition; Reidel

H. Maturana (1980)

10.1103/PhysRevE.93.022114

Thermodynamic aspects of information transfer in complex dynamical systems.

Carlo Cafaro (2016)

Randomness, information, complexity. arXiv 2012

P Grassberger

Complexity Entropy And The Physics Of Information

U. Beyer (2016)

Complexity Metaphors, Models, and Reality

G. Cowan (1994)

The Structure of Science; Harcourt, Brace & World

E Nagel (1961)

10.1063/1.3643065

Introduction to focus issue on "randomness, structure, and causality: measures of complexity from theory to applications".

James P. Crutchfield (2011)

Erstmaligkeit und Bestätigung als Komponenten der pragmatischen Information

Von Weizsäcker (1974)

10.1007/978-3-662-06390-3_13

Phase Transitions in Reservoir-Driven Open Systems with Applications to Lasers and Superconductors

K. Hepp (1973)

Emergence in exact natural science

H. Primas (1998)

10.1007/978-0-387-21830-4_12

Measuring the Strangeness of Strange Attractors

P. Grassberger (1983)

10.1007/BF01217908

The thermodynamic formalism for expanding maps

D. Ruelle (1989)

10.1145/273035.273067

Semantic information retrieval

A. M. Pejtersen (1998)

10.1016/S1874-575X(06)80028-7

Chapter 3 – Stochastic-Like Behaviour in Nonuniformly Expanding Maps

S. Luzzatto (2006)

10.1007/s10701-011-9549-0

Emergence, Reduction and Supervenience: A Varied Landscape

J. Butterfield (2011)

10.1016/j.physd.2010.11.013

Quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and Jacobi fields

Carlo Cafaro (2011)

10.2307/2373370

MARKOV PARTITIONS FOR AXIOM A DIFFEOMORPHISMS.

R. Bowen (1970)

10.1007/S10701-006-9082-8

Contextual Emergence in the Description of Properties

R. C. Bishop (2006)

10.1016/0167-2789(83)90127-6

Symbolic dynamics of noisy chaos

J. Crutchfield (1983)

10.1016/J.LAA.2004.10.026

Robust Perron cluster analysis in conformation dynamics

P. Deuflhard (2005)

10.1609/aimag.v17i3.1230

From Data Mining to Knowledge Discovery in Databases

U. Fayyad (1996)

10.1016/0920-5632(87)90036-3

Fractal measures and their singularities: The characterization of strange sets.

Halsey (1986)

Theory and applications of coupled map lattices

金子 邦彦 (1993)

Applications of Centre

J. Carr (1981)

10.1007/BF01400474

Laserlight — first example of a second-order phase transition far away from thermal equilibrium

R. Graham (1970)

EMERGENCE IN EXACT NATURAL SCIENCES

H. Primas (1998)

10.1093/oxfordhb/9780199957996.013.17

Quantum Models of Cognition and Decision

J. Busemeyer (2012)

Knowledge and Time; Springer: Berlin/Heidelberg, Germany, 2017

H. Primas (2017)

The Collapse of Chaos

I. Stewart (1994)

10.1002/(SICI)1099-0526(199707/08)2:6%3C30::AID-CPLX6%3E3.0.CO;2-L

How nature works: The science of self-organized criticality

D. M. Raup (1997)

10.1109/TSMCC.2004.833293

On understanding understanding. Perception-based processing of NL texts in SCIP systems, or meaning constitution as visualized learning

B. Rieger (2004)

10.1103/RevModPhys.74.47

Statistical mechanics of complex networks

R. Albert (2001)

10.1007/978-3-319-17885-1_100249

Data Mining

K. Rihaczek (2000)

10.1016/j.clinph.2004.12.023

Origin, structure, and role of background EEG activity. Part 3. Neural frame classification

W. Freeman (2005)

Complexity and meaning as a bridge across the Cartesian cut

H Atmanspacher (1994)

Prigogine, I. Self-Organization in Non-Equilibrium Systems

G Nicolis (1977)

10.1007/978-3-319-47370-3

Knowledge and Time

Hans Primas (2017)

10.1007/978-3-642-69365-6

Chemistry, Quantum Mechanics and Reductionism

H. Primas (1981)

10.1007/978-1-4612-4286-4

Chaos, Fractals, and Noise

A. Lasota (1994)

10.1007/978-0-387-87870-6_1

On the Notion of Entropy of a Dynamical System

Y. Sinaĭ (2010)

A formal theory of inductive inference

R. Solomonoff (1964)

10.1016/S0019-9958(64)90131-7

A Formal Theory of Inductive Inference. Part II

R. Solomonoff (1964)

Problems in quantifying self-generated complexity

P. Grassberger (1989)

10.1007/978-0-387-33532-2_2

Methods and Techniques of Complex Systems Science: An Overview

C. Shalizi (2006)

Theory and Applications of Cellular Automata

S. Wolfram (1986)

10.1007/978-3-319-06361-4

Reductionism, Emergence and Levels of Reality: The Importance of Being Borderline

S. Chibbaro (2014)

Does God Play Dice? Penguin

I Stewart (1990)

Principles of Self-Organization

Von Foerster (1962)

Contextual Emergence of Mental States from Neurodynamics

H. Atmanspacher (2005)

10.1023/A:1010388907793

Computational Mechanics: Pattern and Prediction, Structure and Simplicity

C. Shalizi (1999)

10.1163/18756735-90000795

THE VARIETIES OF EMERGENCE: THEIR PURPOSES, OBLIGATIONS AND IMPORTANCE

C. Gillett (2002)

10.1016/J.SHPSB.2014.05.002

Modular localization and the holistic structure of causal quantum theory, a historical perspective

Bert Schroer (2011)

10.1016/S0378-4371(96)00293-2

Statistics and meta-statistics in the concept of complexity

H. Atmanspacher (1997)

10.1007/BF01646342

On the equilibrium states in quantum statistical mechanics

R. Haag (1967)

10.1007/S10699-016-9489-4

The Deluge of Spurious Correlations in Big Data

Cristian S. Calude (2017)

10.1007/BF01609475

Quantum detailed balance and KMS condition

A. Kossakowski (1977)

10.1016/j.concog.2004.07.001

Identifying neural correlates of consciousness: The state space approach

J. Fell (2004)

The Fractal Geometry of Nature, 3rd ed.; Freeman: San Francisco

B. B. Mandelbrot (1983)

Symbolic Dynamics and Cod-ing

David Lind (1995)

10.1007/BF00668821

Toward a quantitative theory of self-generated complexity

P. Grassberger (1986)

10.1016/0034-4877(77)90034-9

Remarks on A-entropy☆

A. Wehrl (1977)

Laser light—First example of a phase transition far away rom equilibrium

R Graham (1970)

The Structure of Science; Harcourt

E. Nagel (1961)

10.1016/0375-9601(75)90353-9

Analogy between higher instabilities in fluids and lasers

H. Haken (1975)

10.1016/S0160-9327(97)88804-7

How nature works: The science of self-organized criticality (copernicus)

E. Bonabeau (1997)

Information : new questions to a multidisciplinary concept

K. Kornwachs (1996)

10.1371/journal.pcbi.1002510

Structural Drift: The Population Dynamics of Sequential Learning

J. Crutchfield (2012)

Emergence or Reduction

A. Beckermann (1992)

Scheingraber, H. (Eds.) Information Dynamics; Plenum

H. Atmanspacher (1991)

Principles of Self-Organization; Pergamon

H. Von Foerster (1962)

10.4324/9780203647417

Encyclopedia of nonlinear science

A. Scott (2006)

Self-organization in non-equilibrium systems

G. Georgiev (2015)

10.1142/6372

Worldviews, Science, and Us: Philosophy and Complexity.

C. Gershenson (2007)

Applications Of Centre Manifold Theory

M. Bosch (2016)

10.1007/978-94-017-2973-4_5

New Metric Invariant of Transitive Dynamical Systems and Automorphisms of Lebesgue Spaces

A. N. Shiryayev (1993)

10.1093/nc/niw012

Can the macro beat the micro? Integrated information across spatiotemporal scales.

Erik P. Hoel (2016)

Emergence or Reduction? De Gruyter

A Beckermann (1992)

10.1016/S0370-1573(01)00025-4

Predictability: a way to characterize complexity

G.Boffetta (2002)

10.1063/1.531279

New methods and structures in the theory of the multi‐mode Dicke laser model

G. Alli (1995)

10.1016/J.PHYSD.2004.11.008

Statistically optimal almost-invariant sets

G. Froyland (2005)

10.1142/S0218127403008636

Pseudo-Deterministic Chaotic Systems

R. Viana (2003)

10.1007/978-3-642-25008-8

Semantic Search over the Web

Roberto De Virgilio (2012)

Being No One

T Metzinger (2003)

10.1515/9781400841356

The structure and dynamics of networks

M. Newman (2006)

10.1007/BF01651541

Stability and equilibrium states

R. Haag (1974)

10.2307/2347530

Finding Groups in Data: An Introduction to Cluster Analysis

L. Kaufman (1990)

10.1088/0031-8949/36/3/032

Self creation of meaning

H. Atlan (1987)

10.1201/9780429502880

Complexity, Entropy And The Physics Of Information

W. H. Zurek (1990)

10.1017/CBO9780511626135

Foundations of Complex-system Theories

S. Auyang (1998)

Quantum Mechanics and Its Emergent Macrophysics

G. Sewell (2002)

Dynamical distance : coarse grains , pattern recognition , and network analysis

B. Gaveaua (2005)

The Mathematical Theory of Communication; University of Illinois Press: Urbana

C. E. Shannon (1949)

Ed.) Theory and Applications of Coupled Map Lattices

K. Kaneko (1993)

Semantic information retrieval. In Information Retrieval: Uncertainty and Logics

G. Amati (1998)

10.1016/S0019-9958(66)80018-9

The Definition of Random Sequences

P. Martin-Löf (1966)

10.1103/PhysRevA.34.253

Deterministic chaos and dynamical instabilities in a multimode cw dye laser.

Atmanspacher (1986)

The Logical Analysis Of Quantum Mechanics

Anja Walter (2016)

Vitànyi, P.M.B. The Google similarity distance

R. L. Cilibrasi (2007)

10.1080/02604027.1997.9972639

Cartesian cut, Heisenberg cut, and the concept of complexity

H. Atmanspacher (1997)

10.1162/1064546041255557

Autopoiesis and Cognition

P. Bourgine (2004)

10.1016/0303-2647(95)01578-7

First conference on foundations of information science: from computers and quantum physics to cells, nervous systems, and societies.

P. Marijuán (1996)

Complexity Measures and Cellular Automata

K. Lindgren (1988)

Complexity measures and cellular automata. Complex Syst

K Lindgren (1988)

Statistical mechanics of complex networks. Rev. Modern Phys

R Albert (2002)

The Collapse of Chaos; Penguin

J. Cohen (1994)

Eds.) Complexity—Metaphors, Models, and Reality

G. A. Cowan (1994)

A Mathematical Theory of Communication

J. W. Shin (2006)

10.1017/S1062798709000738

Foundations of Complex Systems

G. Nicolis (2009)

10.1109/TE.1962.4322250

General System Theory

L. Zadeh (1962)

10.1016/0960-0779(94)90015-9

Fluctuation Spectroscopy

Karl Young (1993)

10.1007/BF01075361

Markov partitions and C-diffeomorphisms

Ya. G. Sinai (1968)

Three approaches to the quantitative definition of complexity

A N Kolmogorov (1965)

Randomness, information, complexity

P. Grassberger (2012)

10.1063/1.3072788

Mental states as macrostates emerging from brain electrical dynamics.

Carsten Allefeld (2009)

10.1016/0096-0551(80)90011-9

Introduction to Automata Theory, Languages and Computation

J. Hopcroft (1979)

10.2307/2323761

Fractal Geometry of Nature

B. Mandelbrot (1977)

10.1007/978-3-642-48647-0_14

Observing Complexity and the Complexity of Observation

J. Crutchfield (1994)

10.1016/c2009-0-06625-2

Philosophy of complex systems

C. Hooker (2011)

10.1016/j.physa.2010.03.028

The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models

Sean A. Ali (2010)

Interpreting the substantive significance of multivariable regression coefficients

J. E. Miller (2008)

Complex Networks: Structure and Dynamics

Shilpa Chakravartula (2014)

10.5860/choice.47-0822

Complexity - A Guided Tour

Melanie Mitchell (2009)

Measuring complexity using information fluctuations

J E Bates (1993)

10.1109/TKDE.2007.48

The Google Similarity Distance

Rudi Cilibrasi (2007)

10.1016/0960-0779(94)90023-X

A comparative classification of complexity measures

R. Wackerbauer (1994)

10.1016/J.BIOSYSTEMS.2006.03.001

Complexity and non-commutativity of learning operations on graphs.

H. Atmanspacher (2006)

10.1007/978-3-642-56861-9

Complex Systems: Chaos and Beyond

K. Kaneko (2001)

10.1073/pnas.91.11.5033

A measure for brain complexity: relating functional segregation and integration in the nervous system.

G. Tononi (1994)

10.1037/A0027157

Horizontal and vertical determination of mental and neural states

Jens Harbecke (2012)

10.1007/978-1-4899-0718-9_30

Science and complexity.

W. Weaver (1948)

10.7551/mitpress/4629.003.0004

Mental Causation

H. Stapp (2007)

10.1103/PhysRevLett.63.105

Inferring statistical complexity.

Crutchfield (1989)

New methods and structures in the theory of the Dicke laser model

G Ali (1995)

Eds.) Proceedings of the Conference on Foundations of Information Science, from computers and quantum physics to cells, nervous systems, and societies

P. Marijuàn (1994)

10.1007/978-3-642-29923-0

The Semantic Web

G. Goos (2011)

10.1145/321356.321363

On the Length of Programs for Computing Finite Binary Sequences

G. Chaitin (1966)

10.1109/MCS.2001.939938

Measures of complexity: a nonexhaustive list

S. Lloyd (2001)

10.1139/p90-105

Pragmatic information and dynamical instabilities in a multimode continuous-wave dye laser

H. Atmanspacher (1990)

This paper is referenced by

10.3390/e19010018

Information and Self-Organization

H. Haken (1988)

10.1007/s11023-020-09516-9

Dynamical Emergence Theory (DET): A Computational Account of Phenomenal Consciousness

Roy Moyal (2020)

10.1007/s10867-020-09543-8

On the emergence of cognition: from catalytic closure to neuroglial closure

José Luis Pérez Velazquez (2020)

10.3390/E21050500

Dynamic Computation in Visual Thalamocortical Networks

Roy Moyal (2019)

10.3390/E22010089

Time Series Complexities and Their Relationship to Forecasting Performance

Mirna P. Ponce-Flores (2020)

10.3390/e22060609

Mathematical Models of Consciousness

Johannes Kleiner (2020)

10.3390/info10090272

Correlations and How to Interpret Them

Harald Atmanspacher (2019)

Dynamical Emergence of Phenomenal Consciousness: an Outline of a Theory

Roy Moyal (2019)