Coarse Graining Shannon and von Neumann Entropies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10372270" target="_blank" >RIV/00216208:11320/17:10372270 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.3390/e19050207" target="_blank" >http://dx.doi.org/10.3390/e19050207</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e19050207" target="_blank" >10.3390/e19050207</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Coarse Graining Shannon and von Neumann Entropies

Popis výsledku v původním jazyce

The nature of coarse graining is intuitively &quot;obvious&quot;, but it is rather difficult to find explicit and calculable models of the coarse graining process (and the resulting entropy flow) discussed in the literature. What we would like to have at hand is some explicit and calculable process that takes an arbitrary system, with specified initial entropy S, and that monotonically and controllably drives the entropy to its maximum value. This does not have to be a physical process, in fact for some purposes it is better to deal with a gedanken-process, since then it is more obvious how the &quot;hidden information&quot; is hiding in the fine-grain correlations that one is simply agreeing not to look at. We shall present several simple mathematically well-defined and easy to work with conceptual models for coarse graining. We shall consider both the classical Shannon and quantum von Neumann entropies, including models based on quantum decoherence, and analyse the entropy flow in some detail. When coarse graining the quantum von Neumann entropy, we find it extremely useful to introduce an adaptation of Hawking&apos;s super-scattering matrix. These explicit models that we shall construct allow us to quantify and keep clear track of the entropy that appears when coarse graining the system and the information that can be hidden in unobserved correlations (while not the focus of the current article, in the long run, these considerations are of interest when addressing the black hole information puzzle).

Název v anglickém jazyce

Coarse Graining Shannon and von Neumann Entropies

Popis výsledku anglicky

The nature of coarse graining is intuitively &quot;obvious&quot;, but it is rather difficult to find explicit and calculable models of the coarse graining process (and the resulting entropy flow) discussed in the literature. What we would like to have at hand is some explicit and calculable process that takes an arbitrary system, with specified initial entropy S, and that monotonically and controllably drives the entropy to its maximum value. This does not have to be a physical process, in fact for some purposes it is better to deal with a gedanken-process, since then it is more obvious how the &quot;hidden information&quot; is hiding in the fine-grain correlations that one is simply agreeing not to look at. We shall present several simple mathematically well-defined and easy to work with conceptual models for coarse graining. We shall consider both the classical Shannon and quantum von Neumann entropies, including models based on quantum decoherence, and analyse the entropy flow in some detail. When coarse graining the quantum von Neumann entropy, we find it extremely useful to introduce an adaptation of Hawking&apos;s super-scattering matrix. These explicit models that we shall construct allow us to quantify and keep clear track of the entropy that appears when coarse graining the system and the information that can be hidden in unobserved correlations (while not the focus of the current article, in the long run, these considerations are of interest when addressing the black hole information puzzle).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

<a href="/cs/project/GB14-37086G" target="_blank" >GB14-37086G: Centrum Alberta Einsteina pro gravitaci a astrofyziku</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Entropy

ISSN

1099-4300

e-ISSN

—

Svazek periodika

19

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

22

Strana od-do

—

Kód UT WoS článku

000404453700025

EID výsledku v databázi Scopus

2-s2.0-85019215805