Tropical limit and the micro-macro correspondence
Abstract
Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents (elements) that is well-behaved with respect to composition. This kind of connection is studied with maps that preserve a monoid structure. The approach highlights an underlying order relation that is explored through the concepts of filter and ideal. Particular attention is paid to asymmetry and duality between max- and min-criteria. Physical implementations are presented through simple examples in thermodynamics and non-equilibrium physics. The phenomenon of ultrametricity, the notion of tropical equilibrium and the role of ground energy in non-equilibrium models are discussed. Tropical symmetry, i.e. idempotence, is investigated.
Cite
@article{arxiv.1701.01144,
title = {Tropical limit and the micro-macro correspondence},
author = {Mario Angelelli},
journal= {arXiv preprint arXiv:1701.01144},
year = {2021}
}
Comments
33 pages. Typos have been corrected, some statements have been clarified. Latest version