# The Nature of Stability in Replicating Systems

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## Abstract

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## 1. Introduction

## 2. Kinetic Stability vs. Thermodynamic Stability

_{2}-O

_{2}mixture, under appropriate conditions, can be extremely persistent and maintained almost indefinitely, despite its non-equilibrium state. In order for reaction to take place, some form of activation, provided by a spark or appropriate catalyst, is necessary. Thus, we term aH

_{2}-O

_{2}mixture (under appropriate conditions) to be kinetically stable due to the high kinetic barrier separating reactants from products.

**Figure 1.**Gibbs energy as a function of the reaction coordinate of A. Under conditions of kinetic control, product X will be favored, while under conditions of thermodynamic control, product Y will be favored.

_{2}-O

_{2}mixture mentioned above is a static one, i.e., no change takes place within that system over time. However, within the category of kinetic stability there is a distinct class of systems whose stability is of a dynamic type, rather than of the more familiar static type. As its name implies, dynamic kinetically stable systems are dynamic, constantly in motion. A river or fountain provides a physical example of the dynamic aspect. A river’s stability is of a dynamic type in that the water that constitutes the river is continually changing—the rate of water flow into the river from its sources equaling the rate of flow out into the sea. Yet the river’s appearance remains constant over time, thereby manifesting stability. As long as the water supply is unimpeded, the river (or fountain) as an entity remains stable. Thus that river exemplifies a physical non-equilibrium steady state. Its stability, a dynamic stability, is based on change, as opposed to lack of change.

## 3. Dynamic Kinetic Stability of Replicating Systems

**Figure 2.**Schematic representation of branching patterns within (a) ‘regular’ (thermodynamic) space (convergent); and within (b) replicator (kinetic) space (divergent).

## 4. Interplay between Dynamic Kinetic Stability and Thermodynamic Stability

## 5. Summary

## Acknowledgements

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Wagner, N.; Pross, A. The Nature of Stability in Replicating Systems. *Entropy* **2011**, *13*, 518-527.
https://doi.org/10.3390/e13020518

**AMA Style**

Wagner N, Pross A. The Nature of Stability in Replicating Systems. *Entropy*. 2011; 13(2):518-527.
https://doi.org/10.3390/e13020518

**Chicago/Turabian Style**

Wagner, Nathaniel, and Addy Pross. 2011. "The Nature of Stability in Replicating Systems" *Entropy* 13, no. 2: 518-527.
https://doi.org/10.3390/e13020518