Statistical mechanics of exploding phase spaces: ontic open systems
File(s)
Author(s)
Jensen, HJ
Pazuki, RH
Pruessner, G
Tempesta, P
Type
Journal Article
Abstract
The volume of phase space may grow super-exponentially ('explosively') with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.
Date Issued
2018-09-14
Date Acceptance
2018-07-24
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
51
Issue
37
Copyright Statement
© 2018 IOP Publishing Ltd. Licensed under a CC BY-NC-ND 3.0 licence (https://creativecommons.org/licences/by-nc-nd/3.0)
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics, Mathematical
Physics
phase space growth rate
super-exponential behaviour
group entropy
max entropy
01 Mathematical Sciences
02 Physical Sciences
Mathematical Physics
Publication Status
Published
Article Number
375002
Date Publish Online
2018-07-24