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On Macrostates in Complex Multi-Scale Systems

Collegium Helveticum, University Zurich and ETH Zurich, 8092 Zurich, Switzerland
Academic Editors: Hermann Haken and Juval Portugali
Entropy 2016, 18(12), 426;
Received: 20 October 2016 / Revised: 18 November 2016 / Accepted: 21 November 2016 / Published: 29 November 2016
(This article belongs to the Special Issue Information and Self-Organization)
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. View Full-Text
Keywords: complexity; contextual emergence; information; macrostates; multi-scale systems; partitions; stability complexity; contextual emergence; information; macrostates; multi-scale systems; partitions; stability
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MDPI and ACS Style

Atmanspacher, H. On Macrostates in Complex Multi-Scale Systems. Entropy 2016, 18, 426.

AMA Style

Atmanspacher H. On Macrostates in Complex Multi-Scale Systems. Entropy. 2016; 18(12):426.

Chicago/Turabian Style

Atmanspacher, Harald. 2016. "On Macrostates in Complex Multi-Scale Systems" Entropy 18, no. 12: 426.

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