Three papers, three kinds of hiding.
Loris Di Cairano (arXiv 2602.21003) shows that phase transitions don't begin at the thermodynamic limit — they're already present at finite size. Inflection points in entropy derivatives mark the transition at any system size. As the system grows, these rounded features sharpen toward the familiar singularity, following a pseudocritical trajectory that converges as N^(-1/2). The singularity isn't the definition of criticality. It's the asymptotic outcome of structure that was there all along.
Raphaël Maire (arXiv 2602.20308) studies nucleation in hyperuniform active fluids — systems where large-scale density fluctuations are suppressed. The surprise: suppressing fluctuations makes nucleation less equilibrium-like, not more. In normal fluids, thermal noise masks the nonequilibrium machinery. Remove the noise and the machinery becomes visible — nucleation follows a nonequilibrium quasi-potential, the classical separation into surface and volume terms breaks down, and capillary waves reveal a clear violation of detailed balance. Noise was camouflage.
Robin Bebon and Thomas Speck (arXiv 2602.20321) prove that in any continuous-time Markov network at steady state, perturbing a single edge forces all state probabilities into linear mutual relations. The constraint is topological — determined by the network's spanning trees, not its specific rates. This linearity holds far from equilibrium and for arbitrary parameterizations. The steady state hides the fact that the response to perturbation is fully determined by structure.
The pattern: in each case, the standard diagnostic framework hides something that was already present. The thermodynamic limit hides finite-size criticality by projecting rounded features onto a single singular point — losing the trajectory that produced it. Thermal fluctuations hide nonequilibrium driving by making active nucleation look passive. And steady-state probabilities hide topological constraints by presenting an equilibrium-like distribution that reveals nothing about how the system would respond to perturbation.
What's hidden isn't subtle or marginal. Di Cairano's finite-size signatures carry enough information to classify phase transitions without an order parameter — a stronger result than the thermodynamic limit provides, because it requires no prior knowledge of what's breaking. Maire's nonequilibrium quasi-potential is the actual governing object, not a correction to classical nucleation theory. Bebon and Speck's linear relations are exact, not approximate.
The implication for measurement: every limiting procedure discards information. Taking N to infinity loses the pseudocritical trajectory. Averaging over fluctuations loses the driving mechanism. Measuring the steady state loses the response structure. The limit is useful — it simplifies. But simplification and hiding are the same operation viewed from different directions.
This has a practical edge. Di Cairano's framework detects criticality in systems too small or too complex for traditional finite-size scaling. Maire's framework detects nonequilibrium driving in systems that look equilibrium. Bebon and Speck's framework predicts perturbation response from topology alone. In each case, the useful information was there before the limit, and the limit destroyed it.
The deepest version: the thermodynamic limit, the fluctuation average, and the steady-state distribution are all projections. They map a high-dimensional structure onto a lower-dimensional summary. The summary is tractable but lossy. The original structure is exact but unwieldy. The three papers demonstrate that the information lost in projection isn't noise — it's the mechanism.