On Identification of Heat and Work in Quantum Many-Body Systems with Local Operations and Classical Communication

Modern quantum thermodynamics faces a fundamental ambiguity: how to distinguish between heat and work when dealing with quantum systems that undergo state changes and measurement-based feedback. This paper addresses this by examining energy extraction via Local Operations and Classical Communication (LOCC) within the Quantum Energy Teleportation (QET) protocol, seeking a rigorous definition of heat that does not rely on traditional, often ambiguous, density matrix changes.

The author utilizes the concept of daemonic ergotropy—the maximum energy extractable from a system given a measurement outcome—as the benchmark for work. By comparing the actual energy extracted during a non-optimized LOCC process to this theoretical maximum, the author identifies the "uncontrollable" energy remaining in the system as heat. This approach treats the nonlocal correlations between spatially separated participants (Alice and Bob) as the source of this heat, which remains inaccessible to the local observer. The author then formalizes this by deriving two types of generalized Clausius inequalities, providing a thermodynamic description of the QET process.

Findings and Significance

The study demonstrates that heat can be defined as the deviation of the actual energy extraction from the optimal daemonic ergotropy. This definition is consistent with the traditional view of heat as uncontrollable energy, while explicitly incorporating quantum information concepts. By applying this to a one-dimensional Kitaev-like model, the author shows that the Clausius inequality in this effective thermodynamics can be used to understand the physical meaning of effective temperature in quantum protocols. This work is significant for the development of future quantum infrastructure, such as energy transfer between distant quantum computers, by providing a theoretical basis for minimizing waste heat.