Abstract

Thermodynamics at the nanoscale is known to differ significantly from its familiar macroscopic counterpart: The possibility of state transitions is not determined by free energy alone but by an infinite family of free-energy-like quantities; strong fluctuations (possibly of quantum origin) allow one to extract less work reliably than what is expected from computing the free-energy difference. However, these known results rely crucially on the assumption that the thermal machine is not only exactly preserved in every cycle but also kept uncorrelated from the quantum systems on which it acts. Here, we lift this restriction: We allow the machine to become correlated with the microscopic systems on which it acts while still exactly preserving its own state. Surprisingly, we show that this possibility restores the second law in its original form: Free energy alone determines the possible state transitions, and the corresponding amount of work can be invested or extracted from single systems exactly and without any fluctuations. At the same time, the work reservoir remains uncorrelated from all other systems and parts of the machine. Thus, microscopic machines can increase their efficiency via clever “correlation engineering” in a perfectly cyclic manner, which is achieved by a catalytic system that can sometimes be as small as a single qubit (though some setups require very large catalysts). Our results also solve some open mathematical problems on majorization which may lead to further applications in entanglement theory.Received 31 August 2018Revised 17 November 2018DOI:https://doi.org/10.1103/PhysRevX.8.041051Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsQuantum statistical mechanicsQuantum thermodynamicsResource theoriesQuantum InformationStatistical Physics

Highlights

  • Thermodynamics, as it is presented in the textbooks, is usually concerned with macroscopic physical systems, like large ensembles of weakly interacting gas molecules

  • We are working within a framework for thermodynamics that is motivated by quantum information theory

  • This framework formulates thermodynamics as a resource theory [27,28]: Given any state of a physical system, together with a set of rules that constrain the agent’s actions, a resource theory asks for the ultimate limits of what is possible, e.g., how much work the agent can extract or what state transitions she can enforce

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Summary

Introduction

Thermodynamics, as it is presented in the textbooks, is usually concerned with macroscopic physical systems, like large ensembles of weakly interacting gas molecules. In this regime, the law of large numbers renders fluctuations mostly irrelevant, and one obtains very precise statistical predictions by computing averages. One of the most important quantities in this regime is the Helmholtz free energy, FðρÞ 1⁄4 hEiρ − TSðρÞ; where hEiρ is the average energy of the system in state ρ and S is its entropy. At constant ambient temperature T and constant volume, transitions between two states are possible if and only if the difference between the free energies. The free-energy difference tells us how much work we can extract, or need to invest, during a thermodynamic state transition

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