Laboratoire de Physique Théorique
Toulouse - UMR 5152

In thermodynamics there are expressions relating work with entropy. We argue that for systems that are finite sized and/or internally correlated, the standard expression involving the von Neumann entropy is inadequate, and we derive the appropriate expression. Our expression reduces to the standard one in the limit of large systems without internal correlations. To make sense of expressions relating work and entropy one may picture an observer who assigns a probability distribution to the system’s energy eigenstates. The entropy is a function of that distribution and thus observer-dependent. The work in the expression is the amount that the given observer can extract. The expressions we give hold whether the observer is a standard thermodynamical observer or a Maxwell’s daemon with extra knowledge, e.g. through being entangled with the system. Our techniques are related to a new approach to information theory known as single-shot information theory, which is currently taking over in quantum information theory.