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Smooth entropy in axiomatic thermodynamics

Weilenmann, Mirjam and Gabriel, Lea Krämer and Faist, Philippe and Renner, Renato (2018) Smooth entropy in axiomatic thermodynamics. In: Thermodynamics in the Quantum Regime. , pp. 773-798. ISBN 978-3-319-99045-3. (Submitted)

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Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including microscopic systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy.

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Additional Information:Part of this research was made possible by the COST MP1209 network. MW is supported by the EPSRC (grant number EP/P016588/1). PhF acknowledges support from the Swiss National Science Foundation (SNSF) through the Early PostDoc.Mobility Fellowship No. P2EZP2 165239 hosted by the Institute for Quantum Information and Matter (IQIM) at Caltech, from the IQIM which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant PHY-1733907), and from the Department of Energy Award de-sc0018407.
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)P/P016588/1
Swiss National Science Foundation (SNSF)P2EZP2 165239
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Department of Energy (DOE)DE-SC0018407
Record Number:CaltechAUTHORS:20190211-151339114
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92839
Deposited By: Bonnie Leung
Deposited On:12 Feb 2019 22:01
Last Modified:03 Oct 2019 20:48

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