Information Dynamics and The Arrow of Time

Time appears to pass irreversibly. In light of CPT symmetry, the Universe's initial condition is thought to be somehow responsible. We propose a model, the stochastic partitioned cellular automaton (SPCA), in which to study the mechanisms and consequences of emergent irreversibility. While their most natural definition is probabilistic, we show that SPCA dynamics can be made deterministic and reversible, by attaching randomly initialized degrees of freedom. This property motivates analogies to classical field theories. We develop the foundations of non-equilibrium statistical mechanics on SPCAs. Of particular interest are the second law of thermodynamics, and a mutual information law which proves fundamental in non-equilibrium settings. We believe that studying the dynamics of information on SPCAs will yield insights on foundational topics in computer engineering, the sciences, and the philosophy of mind. As evidence of this, we discuss several such applications, including an extension of Landauer's principle, and sketch a physical justification of the causal decision theory that underlies the so-called psychological arrow of time.