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We study the slowly varying, non-autonomous quantum dynamics of a translationinvariant spin or fermion system on the lattice $\mathbb Z^d$. This system isassumed to be initially in thermal equilibrium, and we consider realizations ofquasi-static processes in the adiabatic limit. By combining the Gibbsvariational principle with the notion of quantum weak Gibbs states introducedin [Jak\v{s}i\'c, Pillet, Tauber, arXiv:2204.00440], we establish a number ofgeneral structural results regarding such realizations. In particular, we showthat such a quasi-static process is incompatible with the property of approachto equilibrium studied in this previous work.

A note on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems