Relational Dynamics of Action, Energy Conservation, and Entropy

This paper extends a dynamics based on relational consistency to complete histories and many degrees of freedom, and reinterprets stationary action, energy conservation, and entropy increase as different manifestations of a common relational updating process. The preceding paper treated motion as the resolution or transport of relational inconsistency and proposed that self-consistent update sequences may persist through the Persistence Principle. Here, rather than minimizing inconsistency instantaneously, consistency between successive relational states is taken as the fundamental quantity, and the possibility is examined that the continuum limit of its history sum corresponds to action. Using the previously discussed relation dS=ℏdφ, the condition δφ≈0 for a phase-self-consistent history corresponds to δS≈0. Furthermore, if an update quantity is locally transferred between connections in a closed relational network, cancellation of internal transfers may give rise to conservation of a total quantity. Finally, if a conserved excitation is distributed among many microscopic relations and the number of allowed configurations increases, a connection to entropy increase described by SB=kB ln Ω becomes possible. These ideas are presented not as completed derivations, but as a constructive program for deriving action, conservation, and statistical behavior simultaneously from a common discrete update rule.