Work extraction from microcanonical bath

Abstract

We determine the maximal work extractable via a cyclic Hamiltonian process from a positive-temperature (T> 0) microcanonical state of a N≫1 spin bath. The work is much smaller than the total energy of the bath, but can be still much larger than the energy of a single bath spin, e.g. it can scale as . Qualitatively the same results are obtained for those cases, where the canonical state is unstable (e.g., due to a negative specific heat) and the microcanonical state is the only description of equilibrium. For a system coupled to a microcanonical bath the concept of free energy does not generally apply, since such a system —starting from the canonical equilibrium density matrix ρT at the bath temperature T— can enhance the work exracted from the microcanonical bath without changing its state ρT. This is impossible for any system coupled to a canonical thermal bath due to the relation between the maximal work and free energy. But the concept of free energy still applies for a sufficiently large T. Here we find a compact expression for the microcanonical free-energy and show that in contrast to the canonical case it contains a linear entropy instead of the von Neumann entropy.