### Abstract

The generic population that is the subject of our study consists of M indistinguishable members assembled into N groups, or clusters, such that no group is empty. The “member” is the fundamental unit of the population and plays the same role as “monomer” in a polymeric system, or “primary particle” in granular materials. The cluster is characterized by the number of members it contains. We will refer to the number of members in the cluster as the size or mass of the cluster and will use the terms interchangeably. The goal in this chapter is to define a sample space of distributions of clusters and assign a probability measure over it. This probability space of distributions will be called cluster ensemble and forms the basis for the development of generalized thermodynamics. In Chap. 7 we will reformulate the theory on the basis of a more abstract space of distributions.

Original language | English (US) |
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Title of host publication | Understanding Complex Systems |

Publisher | Springer Verlag |

Pages | 23-64 |

Number of pages | 42 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Understanding Complex Systems |
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ISSN (Print) | 1860-0832 |

ISSN (Electronic) | 1860-0840 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Computational Mechanics
- Artificial Intelligence

### Cite this

*Understanding Complex Systems*(pp. 23-64). (Understanding Complex Systems). Springer Verlag. https://doi.org/10.1007/978-3-030-04149-6_2

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*Understanding Complex Systems.*Understanding Complex Systems, Springer Verlag, pp. 23-64. https://doi.org/10.1007/978-3-030-04149-6_2

**The Cluster Ensemble.** / Matsoukas, Themis.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - The Cluster Ensemble

AU - Matsoukas, Themis

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The generic population that is the subject of our study consists of M indistinguishable members assembled into N groups, or clusters, such that no group is empty. The “member” is the fundamental unit of the population and plays the same role as “monomer” in a polymeric system, or “primary particle” in granular materials. The cluster is characterized by the number of members it contains. We will refer to the number of members in the cluster as the size or mass of the cluster and will use the terms interchangeably. The goal in this chapter is to define a sample space of distributions of clusters and assign a probability measure over it. This probability space of distributions will be called cluster ensemble and forms the basis for the development of generalized thermodynamics. In Chap. 7 we will reformulate the theory on the basis of a more abstract space of distributions.

AB - The generic population that is the subject of our study consists of M indistinguishable members assembled into N groups, or clusters, such that no group is empty. The “member” is the fundamental unit of the population and plays the same role as “monomer” in a polymeric system, or “primary particle” in granular materials. The cluster is characterized by the number of members it contains. We will refer to the number of members in the cluster as the size or mass of the cluster and will use the terms interchangeably. The goal in this chapter is to define a sample space of distributions of clusters and assign a probability measure over it. This probability space of distributions will be called cluster ensemble and forms the basis for the development of generalized thermodynamics. In Chap. 7 we will reformulate the theory on the basis of a more abstract space of distributions.

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UR - http://www.scopus.com/inward/citedby.url?scp=85065833807&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04149-6_2

DO - 10.1007/978-3-030-04149-6_2

M3 - Chapter

AN - SCOPUS:85065833807

T3 - Understanding Complex Systems

SP - 23

EP - 64

BT - Understanding Complex Systems

PB - Springer Verlag

ER -