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 $N\gg 1$ 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 $\mathcal{O}(\sqrt{N\ln N})$. Qualitatively 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 {\it not generally} apply, since such a system|starting from the canonical equilibrium density matrix ${\rho }_T$ at the bath temperature $T$|can enhance the work extracted from the microcanonical bath without changing its state ${\rho }_T$. 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 {\it microcanonical free-energy} and show that in contrast to the canonical case it contains a {\it linear entropy} instead of the von Neumann entropy.

6 pages, 1 figure

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• The Physics of Maxwell's demon and information
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• Extracting work from a single heat bath through feedback
• Work extremum principle: Structure and function of quantum heat engines
• Thermodynamics of adiabatic feedback control

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