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Beyond heat baths: Generalized resource theories for small-scale thermodynamics

Yunger Halpern, Nicole and Renes, Joseph M. (2016) Beyond heat baths: Generalized resource theories for small-scale thermodynamics. Physical Review E, 93 (2). Art. No. 022126. ISSN 2470-0045. doi:10.1103/PhysRevE.93.022126.

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Thermodynamics has recently been extended to small scales with resource theories that model heat exchanges. Real physical systems exchange diverse quantities: heat, particles, angular momentum, etc. We generalize thermodynamic resource theories to exchanges of observables other than heat, to baths other than heat baths, and to free energies other than the Helmholtz free energy. These generalizations are illustrated with “grand-potential” theories that model movements of heat and particles. Free operations include unitaries that conserve energy and particle number. From this conservation law and from resource-theory principles, the grand-canonical form of the free states is derived. States are shown to form a quasiorder characterized by free operations, d majorization, the hypothesis-testing entropy, and rescaled Lorenz curves. We calculate the work distillable from—and we bound the work cost of creating—a state. These work quantities can differ but converge to the grand potential in the thermodynamic limit. Extending thermodynamic resource theories beyond heat baths, we open diverse realistic systems to modeling with one-shot statistical mechanics. Prospective applications such as electrochemical batteries are hoped to bridge one-shot theory to experiments.

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Yunger Halpern, Nicole0000-0001-8670-6212
Additional Information:© 2016 American Physical Society. Received 30 September 2015; published 18 February 2016. N.Y.H. is grateful for conversations with Tobias Fritz, Iman Marvian, Markus Müller, Brian Space, and Rob Spekkens. J.M.R. acknowledges helpful conversations with Michael Walter. This work was supported by a Virginia Gilloon Fellowship, an IQIM Fellowship, NSF Grant No. PHY-0803371, the Perimeter Institute for Theoretical Physics, the Swiss National Science Foundation (through the National Centre of Competence in Research Quantum Science and Technology and Grant No. 200020-135048), and the European Research Council (Grant No. 258932). The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center that receives support from the Gordon and Betty Moore Foundation. Research at the Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. N.Y.H. is grateful to Renato Renner for hospitality at ETH Zürich during the development of this paper.
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Funding AgencyGrant Number
Virginia Gilloon FellowshipUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Swiss National Science Foundation (SNSF)200020-135048
European Research Council (ERC)258932
Gordon and Betty Moore FoundationUNSPECIFIED
Industry CanadaUNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20160315-161221220
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Official Citation:Beyond heat baths: Generalized resource theories for small-scale thermodynamics Nicole Yunger Halpern and Joseph M. Renes Phys. Rev. E 93, 022126 – Published 18 February 2016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65377
Deposited By: Tony Diaz
Deposited On:16 Mar 2016 20:32
Last Modified:10 Nov 2021 23:44

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