Isomorphic, Isoentropic and Isocomplex Systems

In a recent blog we introduced the concept of isomorphic and isoentropic system. These are systems in which either the structure or the total entropy remain constant. However, there is another interesting class of systems – isocomplex systems, i.e. systems with a constant value of complexity. In such systems, the interplay of entropy and structure is such that complexity remains constant for certain periods of time. There is of course the trivial case in which complexity is constant, but that is not of much interest. An example is shown below, where in the first part of the plot, on the left hand side, complexity remains relatively flat.

To see what happens in this interval, and excluding the trivial case, let us consider the approximate formula for complexity.

It is interesting to identify which physical phenomena satisfy such condition, i.e. in which structure is created or destroyed with rate opposite to that of entropy.

Established originally in 2005 in the USA, Ontonix is a technology company headquartered in Como, Italy. The unusual technology and solutions developed by Ontonix focus on countering what most threatens safety, advanced products, critical infrastructures, or IT network security - the rapid growth of complexity. In 2007 the company received recognition by being selected as Gartner's Cool Vendor. What makes Ontonix different from all those companies and research centers who claim to manage complexity is that we have a complexity metric. This means that we MEASURE complexity. We detect anomalies in complex defense systems without using Machine Learning for one very good reason: our clients don’t have the luxury of multiple examples of failures necessary to teach software to recognize them. We identify anomalies without having seen them before. Sometimes, you must get it right the first and only time!

4 comments on “Isomorphic, Isoentropic and Isocomplex Systems”

1. Ajay Kumar

How about triple point of water?

Like

2. Ajay

At the triple point of water, three phases coexist. Solid phase is the one which has the strongest structure, whereas the gaseous phase has high entropy and liquid state which is between the two. At this point (temp and pressure) I guess the complexity will remain constant.

Like

• This could be determined using molecular dynamics simulation, modeling the whole system at atomic level.

Like