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 the opposite to the rate of entropy indrease or decrease.