V04·Act I · Consensus
The disagreement Lyapunov
Total disagreement sliding down a free-energy funnel: rugged at the top, inevitable at the bottom, floor at consensus.
The relation on screen
A monotone bounded-below functional on a finite state space terminates, which is an H-theorem in miniature.
Symbols
- disagreement after n repair sweeps
- floor of the funnel, the equilibrium value
loading thermodynamic trace
what to look for · The curve never turns up. Changing the schedule moves how fast the floor is reached but never the floor itself, which is fixed by the topology of the frustration.
Consensus to physics
- 01every repair move lowers total seam disagreement
- 02the functional is bounded below by zero
- 03so it is a Lyapunov function and the process terminates
- 04termination at zero is consensus
In standard physics
The H-theorem
Boltzmann's H, in the role of a monotone functional whose descent defines the direction of the process and whose floor defines equilibrium.
boundary · The functional is not energy and its units are not physical. It is a count of unrepaired seams.