The nature of rare events in biophysical mechanisms, including mutations, underlying evolutionary and ecological processes

Nonequlibrium phenomena constitute much of the world around us, including life itself. They may take millions of years in life of a star, from birth to death, and evolution of galaxies. Nearby, examples entail formation of Earth's biosphere, including the origin and evolution of life, and environmental changes. In a living cell, they may proceed in a fraction of a second via such molecular processes as unfolding of nucleic acids, carriers and controllers of the genetic code, and associated with protein machinery of helicases and ribosomes. Finally, they include the phenomenon of illness, a disorder leading to dysfunction of an organism and eventually to death. However, our understanding of far-from-equilibrium phenomena has not kept pace with its equilibrium counterpart. Recent investigations posed on the microscopic level of statistical mechanics yielded intriguing findings. They incorporate the history of a system and are valid even when the system is disturbed violently from its equilibrium state. A nonequilibrium work relation is one of the most astonishing results among the recent development of nonequilibrium statistical mechanics. We analyze properties of nonequilibrium work distribution including rare events that require less work than the free energy change. The process considered here is adding a single particle into the system. The process is examined from weak to strong nonequilibrium regimes. We determine a relationship of the ratio of rare events to the whole events, and its dominant role in the nonequilibrium work relation. An insight into the nature of rare events is crucial for better understanding of fundamental biophysical mechanisms, including mutations, underlying evolutionary and ecological processes.