**About Sean Devine **

**In looking for a way to approach non equilibrium issues, I stumbled across Chaitin's work on Algorithmic Information Theory (AIT) outlined in the book John Casti's book "Complexification". This introduced me to the works of Gregory Chaitin and ultimately Li and Vitányi’s comprehensive book. While this book is a treasure trove, it is difficult for an outsider to master as the context of much of the development is not clear to a non mathematician. Nevertheless, the book pointed to Kolmogorov's work on algorithmic complexity, probability theory and randomness. So, while the application to economic systems is on the back burner, I realised that AIT provided a useful tool for scientists to look at natural systems.**

However, to apply the approach to the natural world, I needed to master the earlier work of Zurek and Bennett - yet their critical contributions seem to have become lost in the mists of time.

A critical issue in the real world relates to specifying a state that has order or structure and variation. My approach gave rise to what I call the provisional entropy only to find that that Kolmogorov’s Algorithmic Minimum Sufficient Statistic (AMSS) approach (Vereshagin and Vitanyi) had solved the problem. However, I use the term provisional entropy rather than AMSS, as this entropy aligns with the traditional understandings of entropy and provides a path into discussing real non equilibrium systems.

As I discuss here, after developing AIT to address far-from- equilibrium systems, I have been able to show Landauer’s principleis a direct consequence of the Stirling Approximation and the definition of temperature, by actually counting states. The bit that specifies a microstate in a potential energy configuration can be identified as potential thermodynamic entropy. Once such a bit moves to the momentum degrees of freedom, it becomes realised thermodynamic entropy and from the demonstration of Landauer’s principle, carries kBln2 units of entropy per bit. This allowed me to determine the energy and entropy requirements to maintain a system, such as an ecological system distant from equilibrium. As discussed, natural replication processes generate and maintain order in living systems. Over time given variation and selection, a simple natural replicating entity will evolve forming a complex superstructure such as a forest ecology. Such far from equilibrium complex living systems are inevitable given natural laws and replication.

I also show that an economy is a far-from-equilibrium replicating system by starting with a simple hunter gather family, and showing how replication processes and energy drivers generate a sophisticated, interconnected economic system. The further such a system is from equilibrium, the greater is its productivity. But to survive further from equilibrium more energy is required with a greater capability to expel waste. The limited ability to expel carbon dioxide for economic systems that depend on non-renewable sources threatens economic. Is needed to maintain viability. See

J. L. Casti. "Complexification:Explaining a Paradoxical World Through the Science of Surprise. Harpercollins (1995).Li, Ming, and Paul M. B. Vit´anyi, “ An Introduction to Kolmogorov Complexity and Its Applications”, 3rd. ed. New York: Springer-Verlag (2008).

S. D. Devine. The application of algorithmic information theory to noisy patterned strings. Complexity, 12(2):52–58 (2006).

N. K. Vereshchagin and P. M. B. Vitányi. "Kolmogorov's structure functions and model selection". IEEE Transactions on Information Theory, 50(12):3265–3290 (2004).