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SUMMARY:Dynamical maps on quantum Orlicz spaces
DTSTART;VALUE=DATE-TIME:20170904T143000Z
DTEND;VALUE=DATE-TIME:20170904T150000Z
DTSTAMP;VALUE=DATE-TIME:20230207T202800Z
UID:indico-contribution-151@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Wladyslaw Adam Majewski (The Gdansk University)\n\nW
e present a new rigorous approach based on Orlicz spaces for the descripti
on of the statistics of large regular statistical systems\, both classical
and quantum. We emphasize that the presented formalism is applicable to Q
FT!\nThe pair of Orlicz spaces we explicitly use are respectively built on
the exponential function\n(for the description of regular observables) an
d on an entropic type function (for the corresponding states). They form a
dual pair (both for classical and quantum systems). This pair $\\langle L
^{\\cosh - 1}\, L\\log(L+1)\\rangle$ has the advantage of being general en
ough to encompass regular observables\, and specific enough for the latter
Orlicz space to select states with a well-defined entropy function.\nQuan
tum dynamical maps are defined and studied for quantum statistical physics
based on Orlicz spaces. We show that even in the most general non-commuta
tive contexts\, completely positive Markov maps satisfying a natural Detai
led Balance condition\, canonically admit an action on a large class of qu
antum Orlicz spaces. This is achieved by the development of a new interpol
ation technique\, specifically suited to the above context\, for extending
the action of such maps to the appropriate intermediate spaces of the pai
r $\\langle L^\\infty\,L^1\\rangle$.\n\nhttps://zakopane.if.uj.edu.pl/even
t/4/contributions/151/
LOCATION:30
RELATED-TO:indico-event-4@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/151/
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