Relational Time without a Free Arrow: Record Capacity, Negentropy Transport, and Finite Autonomous Maintenance

Relational clocks can order conditional change in a globally stationary or microscopically

reversible description, but ordering is not yet a thermodynamic arrow. We formulate the missing

step as a resource-accounting problem for records, separating clock readability, writable register

capacity, kinetic persistence, active repair, syndrome disposal, controller order, fuel, waste, and open

boundary support. A finite stationary history gives exact conditional motion, while an elementary

obstruction shows that a functional monotone under every transformation and inverse in a two-sided

reversible group is constant on each orbit. For a pointer-preserving controlled interaction, the

acquired record information obeys I(S:Rmem)′

= S(R′

mem)−S(Rmem) and is bounded by the initial

writable capacity log2 dmem−S(Rmem). For closed reversible memory–reservoir dynamics, the

identity ∆NM = ∆S(Eres)−∆I(M:Eres) distinguishes local purification from reservoir entropy and

correlation transport. Exact finite real models then exhibit reversible redundant writing, a finite

controller with a hold window and exact recurrence, symmetric barrier protection, reversible three-bit

majority repair, and the conditional syndrome burden H(Y |L) = 3h2(q)−h2(3q2

−2q3) when the

reference word is known (or the input X is retained together with the decoded datum D= X⊕L).

A separate staged frozen-composition chemical-affinity benchmark evaluates a stationary binary

reset at successive externally specified fuel–waste compositions, giving a nominal error increase

from one to five percent; it is not a joint autonomous stochastic process. Across cycles, marginal

syndrome entropies do not generally add; the fresh burden is H(Yn |Z) = kH(Yk |Y<k,Z),

where Z denotes all retained side information. In a closed classical cyclic-reset architecture whose

sole information sink is a finite waste register W, we prove H(Yn |Z) ≤log2 dW−H(W0), with

W0 initially independent of (Yn,Z); a finite cycle bound follows only when every cycle has a

uniform positive fresh burden. The contribution is the integrated, assumption-controlled dependency

architecture, its exact finite exemplars, and a separately scoped phenomenological benchmark. The

results neither derive a fundamental thermodynamic arrow nor impose a universal finite-memory

lifetime. The finite constructions and resource architecture also do not select complex over real

representations.