Next Article in Journal
Nonlinear Stochastic Control and Information Theoretic Dualities: Connections, Interdependencies and Thermodynamic Interpretations
Next Article in Special Issue
Information Decomposition and Synergy
Previous Article in Journal
A Mean-Variance Hybrid-Entropy Model for Portfolio Selection with Fuzzy Returns
Previous Article in Special Issue
AIM for Allostery: Using the Ising Model to Understand Information Processing and Transmission in Allosteric Biomolecular Systems
Article Menu

Export Article

Open AccessFeature PaperArticle
Entropy 2015, 17(5), 3332-3351; doi:10.3390/e17053332

An Information-Theoretic Perspective on Coarse-Graining, Including the Transition from Micro to Macro

Complex systems group, Department of Energy and Environment, Chalmers University of Technology, SE-41296 Göteborg, Sweden
Academic Editor: Rick Quax
Received: 13 March 2015 / Accepted: 11 May 2015 / Published: 14 May 2015
(This article belongs to the Special Issue Information Processing in Complex Systems)
View Full-Text   |   Download PDF [8499 KB, uploaded 14 May 2015]   |  

Abstract

An information-theoretic perspective on coarse-graining is presented. It starts with an information characterization of configurations at the micro-level using a local information quantity that has a spatial average equal to a microscopic entropy. With a reversible micro dynamics, this entropy is conserved. In the micro-macro transition, it is shown how this local information quantity is transformed into a macroscopic entropy, as the local states are aggregated into macroscopic concentration variables. The information loss in this transition is identified, and the connection to the irreversibility of the macro dynamics and the second law of thermodynamics is discussed. This is then connected to a process of further coarse-graining towards higher characteristic length scales in the context of chemical reaction-diffusion dynamics capable of pattern formation. On these higher levels of coarse-graining, information flows across length scales and across space are defined. These flows obey a continuity equation for information, and they are connected to the thermodynamic constraints of the system, via an outflow of information from macroscopic to microscopic levels in the form of entropy production, as well as an inflow of information, from an external free energy source, if a spatial chemical pattern is to be maintained. View Full-Text
Keywords: information theory; entropy; microscopic; macroscopic; second law; reaction-diffusion; pattern formation information theory; entropy; microscopic; macroscopic; second law; reaction-diffusion; pattern formation
Figures

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Lindgren, K. An Information-Theoretic Perspective on Coarse-Graining, Including the Transition from Micro to Macro. Entropy 2015, 17, 3332-3351.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top