PHY.8:11 - SoTA-Echoing

Baldovin, Gradenigo, Vulpiani and Zanghì, On the foundations of statistical mechanics, Physics Reports 1132 (2025), provides a current synthesis of equilibrium foundations. Sections 3.4-3.5 distinguish selected macroscopic observables and useful sampling from unrestricted dynamical claims; sections 5.1.3-5.1.5 connect quantum states, reduced states and equilibrium weighting. The method uses these distinctions without making one universal equilibration argument a prerequisite.

Compare the excited-count question in :5.1. A physically appropriate equilibrium ensemble gives the same count law that sufficiently repeated microscopic simulation would estimate, with less trajectory computation. Simulation is useful when interactions or preparation invalidate the simple ensemble calculation. A maximum-entropy inference from supplied constraints is another usable route when those are the available grounds; it does not alone establish a relaxation time or response to changed coupling. The different questions determine which contribution is needed.

Corominas-Murtra, Hanel and Jizba, Typicality, entropy and the generalization of statistical mechanics examines extensions of typicality beyond the usual independent-constituent setting. Its distinction between probability concentration and unweighted state counts supports :4.4. The present worked calculations use ordinary finite probabilities; generalized entropy is not required for their decisions. Reopen the concentration argument when the changing alternatives or dependencies defeat its current assumptions.

Korbel and colleagues, Quo vadis, stochastic thermodynamics?, 2026, examines hidden variables, memory and limits of thermodynamic interpretation. Sections II and V matter here: a reduced stochastic description may retain memory, and observable irreversibility does not automatically determine physical dissipation. Use a physical energetic account for a heat claim. For the transport question in :5.3, the density-current account and its diffusion reduction answer the same late-time mean-square question; the current adds useful content when the early response is required. A larger microscopic simulation would cost more without improving this already solvable comparison.

The examples are explicit constructions of the method, not reports of validation of particular devices. More demanding equilibrium, quantum or driven-system questions can require specialized physical and mathematical results. Their use retains the preparation, observable and time conditions that make the result transferable.