Evolution algebras generated by Gibbs measures

Abstract

In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the function spaces (cell spaces) defined by graphs and state spaces and Gibbs measure µ. For finite graphs we find some evolution subalgebras and other useful properties of the algebras. We obtain a structure theorem for evolution algebras when graphs are finite and connected. We prove that for a fixed finite graph, the function spaces has a unique algebraic structure since all evolution algebras are isomorphic to each other for whichever Gibbs measures assigned. When graphs are infinite graphs then our construction allows a natural introduction of thermodynamics in studying of several systems of biology, physics and mathematics by theory of evolution algebras.

Evolution algebras of arbitrary dimension and their decompositions

“…In the last years, many different aspects of the theory of evolution algebras have seen considered. For instance, in [19] evolution algebras are associated to function spaces defined by Gibbs measures on a graph, providing a natural introduction of thermodynamics in the study of several systems in biology, physics and mathematics. On the other hand, chains of evolution algebras (i.e.…”

The Jacobson radical of an evolution algebra

“…Algebraic notions such as nilpotency and solvability may be interpreted biologically as the fact that some of the original gametes (or generators) become extinct after certain generations, and these algebraic properties have been studied in [8,6,30,36,9,17,12]. Moreover evolution algebras associated with function spaces defined by Gibbs measures on a graph are considered in [29], to provide a natural introduction of thermodynamics in the studying of several systems in Biology, Physics and Mathematics. On the other hand, chains of evolution algebras (i.e.…”

On the Property of Subalgebras of Evolution Algebras

“…Recently, Rozikov and Tian [12] studied algebraic structures of evolution algebras associated with Gibbs measures defined on some graphs. In the papers [2], [5], [9] derivations, some properties of chain of evolution algebras and dibaricity of evolution algebras were studied.…”