**95**(2011) 60004

## Work extraction from microcanonical bath

^{1}
Yerevan Physics Institute - Alikhanian Brothers Street 2, Yerevan 375036, Armenia

^{2}
Laboratoire de Physique Statistique et Systèmes Complexes, ISMANS - 44 ave. Bartholdi, 72000 Le Mans, France, EU

^{a}
armen.allahverdyan@gmail.com

Received:
24
June
2011

Accepted:
3
August
2011

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 ρ_{T} at the bath temperature *T*— can enhance the work exracted from the microcanonical bath without changing its state ρ_{T}. 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.

PACS: 05.30.-d – Quantum statistical mechanics / 05.70.-a – Thermodynamics / 07.20.Pe – Heat engines; heat pumps; heat pipes

*© EPLA, 2011*