Local thermal operations and classical communication

In quantum thermodynamics, understanding the interplay between locality, thermal constraints, and communication remains an open challenge. In this manuscript, we introduce local thermal operations and classical communication (LTOCC), an operational framework that unifies the distant laboratories paradigm with thermodynamic restrictions, defining the fundamental limits on transformations between spatially separated systems. We establish a hierarchy of LTOCC protocols, demonstrating inclusion relations between different levels and revealing their deep connection to semilocal thermal operations. To formalize this framework, we develop thermal tensors and bithermal tensors, extending stochastic and tristochastic tensors to thermodynamic settings and providing new mathematical tools for constrained quantum processes. Finally, we present limitations imposed by LTOCC on single- and multicopy CHSH scenario, demonstrating no violation in the former and a gap between thermal and athermal local operations in the latter with respect to their capability to detect entanglement.