Changes dynamics in real complex (or like biological) world should have, in our opinion, more complex curves as designed by thermodynamics. May be, in a close system without historically informed pathway dynamics could be given by one trajectory scaled by abscissa and ordinate. But if to reach another complex metastable state, observing an open system, with exchange making energetic, matter and information balance, we could picture each change with 3 correlated strands: energy, matter and information. Balances are to make with the environment and graph is ideally made simple and coincident this may not be the case.
Energetic strand would consider the need of energy of activation required to get out a metastable state end for a while in another (they should previous and ending ones exist. Anyhow all is expressed in energetic values and their are correlations, balances and equalities involve environment (for resources and as dumps possibly inducing there other transformations (trickling down).
Matter's strand is here pictured as growing in energy and complexity with correlations between energy and matter. But in focused or reduced reality not equal and often with low energetic efficiency (balance consider resources of energy and matter picked in the environment, because system (or part of a larger system is open). The changes can come soon or later, according the variable effect of memory or hysteresis (or configuration of the structure of the system, especially thinking about its reactive part). Considering also for matter (but we would have to consider that the quality have change(while the amount of quantities evolved). Meanwhile the label of amount of matter have or not change according human observer.
Information there can also be imported or exported from environment (including human manipulations) but in the subsystem, consisting in the properties (that for physical world, cannot be so easily determined at will). It depends on the relative configuration (maps) of matter playing as structure and matter delivering or exchanging energy. Information also follow some rules, balances and principles like entropy (which is the energetic expression of trend to more disorder.