Generalized Thermodynamics

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The basis of all of our development up to this point has been the cluster ensemble, a discrete ensemble that generates every possible distribution of integers i with fixed zeroth and first order moments. Thermodynamics arises naturally in this ensemble when M and N become very large. In this chapter we will reformulate the theory on a mathematical basis that is more abstract and also more general. The key idea is as follows. If we obtain a sample from a given distribution h 0 , the distribution of the sample may be, in principle, any distribution h that is defined in the same domain. This sampling process defines a phase space of distributions h generated by sampling distribution h 0 . We will introduce a sampling bias via a selection functional W to define a probability measure on this space and obtain its most probable distribution. When the generating distribution h 0 is chosen to be exponential, the most probable distribution obeys thermodynamics. Along the way we will make contact with Information Theory, Bayesian Inference, and of course Statistical Mechanics.

Original languageEnglish (US)
Title of host publicationUnderstanding Complex Systems
PublisherSpringer Verlag
Pages197-239
Number of pages43
DOIs
StatePublished - Jan 1 2018

Publication series

NameUnderstanding Complex Systems
ISSN (Print)1860-0832
ISSN (Electronic)1860-0840

All Science Journal Classification (ASJC) codes

  • Software
  • Computational Mechanics
  • Artificial Intelligence

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