Fundamental work cost of quantum processes

Presenting Author: Philippe Faist, California Institute of Technology
Contributing Author(s): Renato Renner

Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nano scale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure---the coherent relative entropy---which measures information relative to the Gibbs weight of each microstate. The coherent relative entropy enjoys properties expected from an information measure, and in the limit of many independent copies (i.i.d. limit), we obtain the difference of the quantum relative entropies. The generality of our framework ensures not only that our results hold in the context of other thermodynamic frameworks such as thermal operations, but also in any information-theoretic resource theory where a given operator is to be preserved by free operations. We also derive a new upper bound on the amount of work which can be extracted in a state transition, instead of requiring a specific process to be implemented. From our microscopic thermodynamic model, we recover the macroscopic second law as emergent. Our approach furthermore may be consistently applied at any level of knowledge, for instance, from either the microscopic or macroscopic observer's point of view, clarifying the role of the observer in thermodynamics and allowing to systematically analyze Maxwell-demon-like examples.

Read this article online: https://arxiv.org/abs/1709.00506

(Session 5 : Thursday from 5:00pm - 7:00 pm)


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