The work value of stochastic independence in single-shot thermodynamics

Markus P. Mueller, Michele Pastena

Published 2014-09-10Version 1

In thermodynamics, the interplay of information and energy determines the amount of work that can be extracted from a quantum system, and more generally, the possibility or impossibility of state transitions. While the usual free energy fully captures this relation in the thermodynamic limit, it has recently been shown that the situation is different in the regime of small or strongly correlated systems: there is an infinite family of free energies, related to the Renyi entropies, which constitutes a family of "second laws" constraining transitions in cyclic processes. In this work, we show that there is another resource which is relevant in the micro regime, namely stochastic independence: allowing to create correlations between initially uncorrelated catalysts, without changing their individual states, unlocks all state transitions that are otherwise only possible in the thermodynamic limit. This adds a novel twist to Bennett's suggestion of an "information battery": in addition to pure bits, also absence of correlation between bits can be used to extract additional work from small quantum systems. Surprisingly, this drives the battery further away from equilibrium instead of thermalizing it. Our result also yields an operational non-asymptotic characterization of von Neumann entropy in terms of a majorization relation which generalizes the trumping relation from entanglement theory.