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The resource theory of informational nonequilibrium in thermodynamics

Gour, Gilad and Müller, Markus P. and Narasimhachar, Varun and Spekkens, Robert W. and Yunger Halpern, Nicole (2015) The resource theory of informational nonequilibrium in thermodynamics. Physics Reports, 583 . pp. 1-58. ISSN 0370-1573. doi:10.1016/j.physrep.2015.04.003.

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We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degenerate). In this case, the only free operations are those that add noise to the system (or implement a reversible evolution) and the only nonequilibrium states are states of informational nonequilibrium, that is, states that deviate from the maximally mixed state. The degree of this deviation we call the state’s nonuniformity; it is the resource of interest here, the fuel that is consumed, for instance, in an erasure operation. We consider the different types of state conversion: exact and approximate, single-shot and asymptotic, catalytic and noncatalytic. In each case, we present the necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves. We also review the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies, and that of quantifying the gap between the nonuniformity one must expend to achieve a single-shot state preparation or state conversion and the nonuniformity one can extract in the reverse operation. Quantum state-conversion problems in this resource theory can be shown to be always reducible to their classical counterparts, so that there are no inherently quantum-mechanical features arising in such problems. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible.

Item Type:Article
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URLURL TypeDescription Paper
Müller, Markus P.0000-0002-0299-952X
Yunger Halpern, Nicole0000-0001-8670-6212
Additional Information:© 2015 Elsevier B.V. Accepted 28 April 2015; Available online 11 May 2015. The authors would like to thank Fernando Brandão, Oscar Dahlsten, Nilanjana Datta, Lídia del Rio, Jonathan Oppenheim and Joe Renes for discussions. Research at Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. GG and VN are supported by the Government of Canada through NSERC. This work has been supported by the COST network.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Record Number:CaltechAUTHORS:20150807-085226114
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Official Citation:Gilad Gour, Markus P. Müller, Varun Narasimhachar, Robert W. Spekkens, Nicole Yunger Halpern, The resource theory of informational nonequilibrium in thermodynamics, Physics Reports, Volume 583, 2 July 2015, Pages 1-58, ISSN 0370-1573, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:59301
Deposited By: Tony Diaz
Deposited On:07 Aug 2015 16:02
Last Modified:10 Nov 2021 22:18

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