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By computing the local energy expectation values with respect to some localmeasurement basis we show that for any quantum system there are twofundamentally different contributions: changes in energy that do not alter thelocal von Neumann entropy and changes that do. We identify the former as workand the latter as heat. Since our derivation makes no assumptions on the systemHamiltonian or its state, the result is valid even for states arbitrarily farfrom equilibrium. Examples are discussed ranging from the classical limit topurely quantum mechanical scenarios, i.e. where the Hamiltonian and the densityoperator do not commute.

Local effective dynamics of quantum systems: A generalized approach to work and heat