Hidden kinetic correlations control collective phases of entropy-conditioned histories

Abstract

Visible dynamics and mean dissipation need not determine the collective phases of rare histories. We construct local Markov models with identical ordinary visible path distributions, stationary states, mean entropy production, mean jump activity and driving affinities, yet different phases when histories are weighted by their full entropy production. Visible configurations modulate hidden driven cycles, whose exact elimination turns kinetic correlations into interactions. A positive spectral reduction separates hidden relaxation from collective modes. Periodic binary models retain opposite phases with entropy variances matched at every observation time. For conserved particles, a pair matches the first two joint cumulants of entropy and hidden activity at every observation time, yet selects segregation or a fluctuating state with suppressed long-wavelength density noise. Bound-state transport and fermionic evolution determine their contrasting dynamics. At a clean Ising critical midpoint, the entropy source couples quadratically to the thermal perturbation, making the fourth cumulant the first to detect the critical susceptibility. Its rate per site grows logarithmically, with an exact cutoff set by system size and observation time. For two quenched disorder ensembles, exact sample-response formulas and numerical evidence support a finite fourth-cumulant density despite very slow relaxation; a weak-disorder continuum response admits a controlled Borel sum. A common positive hidden eigenvector characterizes autonomous selected dynamics. When this condition fails, a finite network develops visible memory while preserving its ordinary visible process and mean diagnostics. These results identify kinetic information missed by aggregate thermodynamic observations.