  Life on earth is distinguished by long-lived correlations in time. The
patterns of material organization that characterize living organisms today are
contingent on events that occurred billions of years ago. This contingency is a
necessary component of Darwinian evolution: patterns in the present inherit
some of their features from those in the past. Despite its central role in
biology, heritable information is difficult to recognize in prebiotic systems
described in the language of chemistry or physics. Here, we consider one such
description based on continuous-time Markov processes and investigate the
persistence of heritable information within large sets of dynamical systems.
While the microscopic state of each system fluctuates incessantly, there exist
few systems that relax slowly to their stationary distribution over much longer
times. These systems, selected for their persistence, are further distinguished
by their mesoscopic organization, which allows for accurate course grained
descriptions of their dynamics at long times. The slow relaxation of these
stable patterns is made possible by dissipative currents fueled by
thermodynamic gradients present in the surrounding reservoirs. We show how the
rate of entropy production within a system sets an upper bound on the lifetime
of its persistent patterns. We also consider the probability of finding
persistence within large sets of dynamical systems. We show that physical
constraints based on continuity and locality can strongly influence the
probability of persistence and its dependence on system size. Finally, we
describe how heritable information can be quantified in practice using
universal compression algorithms. We demonstrate this approach on an
experimental system of magnetically-driven, colloidal rollers and discuss the
application of these methods to origins of life research.
