The origin of Life on Earth is the greatest unsolved mystery in the history of science. In spite of progress in almost every scientific endeavor, we still have no clear theory, model, or framework to understand the processes that led to the emergence of life on Earth. Understanding such a processes would provide key insights into astrobiology, planetary science, geochemistry, evolutionary biology, physics, and philosophy. To date, most research on the origin of life has focused on characterizing and synthesizing the molecular building blocks of living systems. This bottom-up approach assumes that living systems are characterized by their component parts, however many of the essential features of life are system level properties which only manifest in the collective behavior of many components. In order to make progress towards solving the origin of life new modeling techniques are needed. In this dissertation I review historical approaches to modeling the origin of life. I proceed to elaborate on new approaches to understanding biology that are derived from statistical physics and prioritize the collective properties of living systems rather than the component parts. In order to study these collective properties of living systems, I develop computational models of chemical systems. Using these computational models I characterize several system level processes which have important implications for understanding the origin of life on Earth. First, I investigate a model of molecular replicators and demonstrate the existence of a phase transition which occurs dynamically in replicating systems. I characterize the properties of the phase transition and argue that living systems can be understood as a non-equilibrium state of matter with unique dynamical properties. Then I develop a model of molecular assembly based on a ribonucleic acid (RNA) system, which has been characterized in laboratory experiments. Using this model I demonstrate how the energetic properties of hydrogen bonding dictate the population level dynamics of that RNA system. Finally I return to a model of replication in which replicators are strongly coupled to their environment. I demonstrate that this dynamic coupling results in qualitatively different evolutionary dynamics than those expected in static environments. A key difference is that when environmental coupling is included, evolutionary processes do not select a single replicating species but rather a dynamically stable community which consists of many species. Finally, I conclude with a discussion of how these computational models can inform future research on the origins of life.

What makes living systems different than non-living ones? Unfortunately this question is impossible to answer, at least currently. Instead, we must face computationally tangible questions based on our current understanding of physics, computation, information, and biology. Yet we have few insights into how living systems might quantifiably differ from their non-living counterparts, as in a mathematical foundation to explain away our observations of biological evolution, emergence, innovation, and organization. The development of a theory of living systems, if at all possible, demands a mathematical understanding of how data generated by complex biological systems changes over time. In addition, this theory ought to be broad enough as to not be constrained to an Earth-based biochemistry. In this dissertation, the philosophy of studying living systems from the perspective of traditional physics is first explored as a motivating discussion for subsequent research. Traditionally, we have often thought of the physical world from a bottom-up approach: things happening on a smaller scale aggregate into things happening on a larger scale. In addition, the laws of physics are generally considered static over time. Research suggests that biological evolution may follow dynamic laws that (at least in part) change as a function of the state of the system. Of the three featured research projects, cellular automata (CA) are used as a model to study certain aspects of living systems in two of them. These aspects include self-reference, open-ended evolution, local physical universality, subjectivity, and information processing. Open-ended evolution and local physical universality are attributed to the vast amount of innovation observed throughout biological evolution. Biological systems may distinguish themselves in terms of information processing and storage, not outside the theory of computation. The final research project concretely explores real-world phenomenon by means of mapping dominance hierarchies in the evolution of video game strategies. Though the main question of how life differs from non-life remains unanswered, the mechanisms behind open-ended evolution and physical universality are revealed.