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Laws of thermodynamics beyond the von Neumann regime

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A recent development in
information theory is the generalisation of quantum Shannon information theory
to the operationally motivated smooth entropy information theory, which
originates in quantum cryptography research. In a series of papers the first
steps have been taken towards creating a statistical mechanics based on smooth
entropy information theory. This approach turns out to allow us to answer
questions one might not have thought were possible in statistical mechanics,
such as how much work one can extract in a given realisation, as a function of
the failure-probability. This is in contrast to the standard approach which
makes statements about average work. Here we formulate the laws of
thermodynamics that this new approach gives rise to. We show in particular that
the Second Law needs to be tightened. The new laws are motivated by our main
quantitative result which states how much work one can extract or must invest
in order to affect a given state change with a given probability of success.
For systems composed of very large numbers of identical and uncorrelated
subsystems, which we call the von Neumann regime, we recover the standard von
Neumann entropy statements.

Joint work with Egloff, Renner and Vedral