Fig. 1: Thermalization setting.

Thermalization of a region R of an equilibrated lattice V via stochastic collisions with an external bath B (red). The collisions are modeled as randomly distributed, energy-preserving unitary interactions between R and B, where these interactions could be either between single subsystems of B (top) or multiple ones (bottom). Our framework is inspired by the resource-theoretic framework of thermal operations^54,55, which have been used to investigate a wide variety of questions, such as the notion of work for microscopic systems^35,56, the quantum fluctuation theorems⁵⁷, the third law^58,59, and several other topics^60,61,62.