arXiv:2611.13124v1 Announce Type: new Abstract: The Kubo--Martin--Schwinger (KMS) condition provides an intrinsic characterization of thermal equilibrium, both in quantum and classical statistical mechanics. In this work, we establish stability of the KMS condition through the quantum-to-classical limit for one-dimensional defocusing Bose gases. More precisely, we consider scaled quantum KMS states in the (mean-field) semiclassical regime and prove that every associated Wigner measure satisfies the classical KMS condition corresponding to the nonlinear Schr\"odinger Hamiltonian. This result extends to an infinite-dimensional setting an earlier derivation of the classical KMS condition for finite-dimensional Bose--Hubbard systems. It also provides a complementary perspective on the derivation of nonlinear Gibbs measures from many-body quantum statistical mechanics.
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