Entropic equality for worst-case work at any protocol speed

A new equality which depends on the maximum entropy describes the worst-case amount of work done by finite-dimensional quantum systems.

New Journal of Physics 19, 43013 (2017)

O. Dahlsten, M. Choi, D. Braun, A. Garner, N. Halpern, V. Vedral

Entropic equality for worst-case work at any protocol speed

We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath. It has the form ‘worst-case work = penalty— optimum’. The equality holds for all rates of changing the Hamiltonian and can be used to derive the optimum by setting the penalty to 0. The optimum term contains the max entropy of the initial state, rather than the von Neumann entropy, thus recovering recent results from single-shot statistical mechanics. Energy coherences can arise during the protocol but are assumed not to be present initially. We apply the equality to an electron box.

More in Information thermodynamics

  • Foundations of Physics

    A Hamiltonian recipe

    An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.

  • Proceedings of the Royal Society A

    Quantum thermodynamics

    Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.

  • Physical Review Letters

    Photonic Maxwell's demon

    With inspiration from Maxwell’s classic thought experiment, it is possible to extract macroscopic work from microscopic measurements of photons.

  • New Journal of Physics

    A measure of majorization

    Single-shot information theory inspires a new formulation of statistical mechanics which measures the optimal guaranteed work of a system.