Heat and Work in Quantum Thermodynamics: a Cybernetic Approach

We present a new proposal for distinguishing heat from work based on a control-theoretic observability decomposition. We derive a Hermitian operator representing instantaneous dissipation of observable energy, and suggest a generalization of the von-Neumann entropy which can account for the model-uncertainty also present in pure states if the measured observables are informationally incomplete. In this view, the transition from a fundamental to a thermodynamic model consists in mapping the fundamental density matrix to an effective one, generally of lower dimension, encoding only what is observable given the constraints of our sensor and actuator capabilities. The generalized entropy captures the information loss incurred in this mapping. The theory is illustrated for the central spin model, where we show that the application of external controls can increase the size of thermal fluctuations and lower the entropy.