When dissipative steady states admit thermodynamic occupation laws
arXiv:2608.26621
2026
Architecture
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper gives a constructive method for embedding an approximately thermodynamic occupation manifold inside a globally dissipative Markov steady state. Its transferable mechanism is sector separation: exclude an entropy-producing reset state from the conditional manifold, impose an exact potential difference on conditional rate ratios, and use rapid reset to obtain a calibrated occupation law without eliminating full-graph circulation. This can become a stochastic latent or routing layer whose conditional probabilities follow neural energy logits while an auxiliary reset sector maintains mixing and exploration. The paper also supplies a diagnostic with a sharp scaling signature: near autonomous redistribution, integrability defects are linear in residual cycle current while entropy production is quadratic.
Ideas from this paper
✗ Failed on benchmark
2026
Add a finite-state stochastic latent layer with conditional states i=1,...,K and an auxiliary reset state 0. The network predicts thermodynamic logits X_i, while transition rates are constructed so that the conditional stationary distribution approaches p_i=exp(X_i)/Z_C under rapid reset, even though the full latent graph retains directed probability currents. This creates a calibrated stochastic layer with controllable mixing and a separate mechanism for maintaining exploration.
Useful7/10
Difficulty6/10
Novelty8/10
Unverified
2026
For a neural stochastic state-space model or discrete diffusion sampler, monitor whether learned transition logits admit a global scalar potential on the active latent manifold. Penalize residual cycle affinities in the conditional sector, but leave reset cycles unpenalized so the model can retain useful dissipative mixing. The distinctive prediction is a linear decrease of integrability error with residual cycle current and a quadratic decrease of entropy production near autonomous…
Useful6/10
Difficulty5/10
Novelty7/10