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This was proved by showing that the additivity of minimum output entropy for all channels doesn't hold, [2] which is an equivalent conjecture. Nonetheless, the additivity of the Holevo information is shown to hold for the quantum depolarizing channel, [ 3 ] and an outline of the proof is given below.
The inspiration for adopting the word entropy in information theory came from the close resemblance between Shannon's formula and very similar known formulae from statistical mechanics. In statistical thermodynamics the most general formula for the thermodynamic entropy S of a thermodynamic system is the Gibbs entropy
major void: 5 23 h 48 m −24° 39′ 53.0 34.8 Aquarius/Sculptor: major void SRSS1 Void 3 (Sculptor Void) 6 3 h 56 m −20° 11′ 56.5 32.0 Eridanus: major void: 7 3 h 17 m −11° 40′ 77.2 25.5 Eridanus: major void: 8 23 h 20 m −12° 32′ 83.9 27.8 Aquarius: major void: 9 3 h 06 m −13° 47′ 114.6 39.0 Eridanus: major void: 10 0 h 26 ...
For an open thermodynamic system in which heat and work are transferred by paths separate from the paths for transfer of matter, using this generic balance equation, with respect to the rate of change with time of the extensive quantity entropy , the entropy balance equation is: [54] [55] [note 1] = = ˙ ^ + ˙ + ˙ where = ˙ ^ is the net rate ...
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems.
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface (cf. closed-cell ...
The KBC Void (or Local Hole) is an immense, comparatively empty region of space, named after astronomers Ryan Keenan, Amy Barger, and Lennox Cowie, who studied it in 2013. [1] The existence of a local underdensity has been the subject of many pieces of literature and research articles.
The Local Void is a vast, empty region of space, lying adjacent to the Local Group. [ 3 ] [ 4 ] Discovered by Brent Tully and Rick Fisher in 1987, [ 5 ] the Local Void is now known to be composed of three separate sectors, separated by bridges of "wispy filaments ". [ 4 ]