Axiomatic relation between thermodynamic and information-theoretic entropies

Mirjam Weilenmann; Lea Krämer; Philippe Faist; Renato Renner

doi:10.1103/PhysRevLett.117.260601

Axiomatic relation between thermodynamic and information-theoretic entropies

Mirjam Weilenmann, Lea Krämer, Philippe Faist, Renato Renner

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory.

Original language	English
Article number	260601
Number of pages	6
Journal	Physical Review Letters
Volume	117
Issue number	26
DOIs	https://doi.org/10.1103/PhysRevLett.117.260601
Publication status	Published - 22 Dec 2016

Keywords

quant-ph
cond-mat.stat-mech

Access to Document

10.1103/PhysRevLett.117.260601

PhysRevLett.117.260601Final published version, 166 KBLicence: CC BY

Cite this

@article{80a875bb01f24f4bb134f6ed72e00e37,

title = "Axiomatic relation between thermodynamic and information-theoretic entropies",

abstract = "Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory.",

keywords = "quant-ph, cond-mat.stat-mech",

author = "Mirjam Weilenmann and Lea Kr{\"a}mer and Philippe Faist and Renato Renner",

year = "2016",

month = dec,

day = "22",

doi = "10.1103/PhysRevLett.117.260601",

language = "English",

volume = "117",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "26",

}

TY - JOUR

T1 - Axiomatic relation between thermodynamic and information-theoretic entropies

AU - Weilenmann, Mirjam

AU - Krämer, Lea

AU - Faist, Philippe

AU - Renner, Renato

PY - 2016/12/22

Y1 - 2016/12/22

N2 - Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory.

AB - Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory.

KW - quant-ph

KW - cond-mat.stat-mech

U2 - 10.1103/PhysRevLett.117.260601

DO - 10.1103/PhysRevLett.117.260601

M3 - Article

VL - 117

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 26

M1 - 260601

ER -