Jaynes' principle for quantum Markov processes: generalized Gibbs-von Neumann states rule

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00367546" target="_blank" >RIV/68407700:21340/23:00367546 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1140/epjp/s13360-023-04272-y" target="_blank" >https://doi.org/10.1140/epjp/s13360-023-04272-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/s13360-023-04272-y" target="_blank" >10.1140/epjp/s13360-023-04272-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Jaynes' principle for quantum Markov processes: generalized Gibbs-von Neumann states rule

Popis výsledku v původním jazyce

We prove that any asymptotics of a finite-dimensional quantum Markov processes can be formulated in the form of a generalized Jaynes' principle in the discrete as well as in the continuous case. Surprisingly, we find that the open-system dynamics does not require maximization of von Neumann entropy. In fact, the natural functional to be extremized is the quantum relative entropy and the resulting asymptotic states or trajectories are always of the exponential Gibbs-like form. Three versions of the principle are presented for different settings, each treating different prior knowledge: for asymptotic trajectories of fully known initial states, for asymptotic trajectories incompletely determined by known expectation values of some constants of motion and for stationary states incompletely determined by expectation values of some integrals of motion. All versions are based on the knowledge of the underlying dynamics. Hence, our principle is primarily rooted in the inherent physics and it is not solely an information construct. The found principle coincides with the MaxEnt principle in the special case of unital quantum Markov processes. We discuss how the generalized principle modifies fundamental relations of statistical physics.

Název v anglickém jazyce

Jaynes' principle for quantum Markov processes: generalized Gibbs-von Neumann states rule

Popis výsledku anglicky

We prove that any asymptotics of a finite-dimensional quantum Markov processes can be formulated in the form of a generalized Jaynes' principle in the discrete as well as in the continuous case. Surprisingly, we find that the open-system dynamics does not require maximization of von Neumann entropy. In fact, the natural functional to be extremized is the quantum relative entropy and the resulting asymptotic states or trajectories are always of the exponential Gibbs-like form. Three versions of the principle are presented for different settings, each treating different prior knowledge: for asymptotic trajectories of fully known initial states, for asymptotic trajectories incompletely determined by known expectation values of some constants of motion and for stationary states incompletely determined by expectation values of some integrals of motion. All versions are based on the knowledge of the underlying dynamics. Hence, our principle is primarily rooted in the inherent physics and it is not solely an information construct. The found principle coincides with the MaxEnt principle in the special case of unital quantum Markov processes. We discuss how the generalized principle modifies fundamental relations of statistical physics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10306 - Optics (including laser optics and quantum optics)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

EUROPEAN PHYSICAL JOURNAL PLUS

ISSN

2190-5444

e-ISSN

—

Svazek periodika

138

Číslo periodika v rámci svazku

657

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

12

Strana od-do

1-12

Kód UT WoS článku

001038695400003

EID výsledku v databázi Scopus

2-s2.0-85166019573