Information Theory and Thermodynamics of Light Part II. Principles of Information Thermodynamics

Ingarden, Román

doi:10.1002/prop.19650131202

Cited by 34 publications

(4 citation statements)

References 20 publications

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“…Our approach points toward following developments: state parameters ζ(t) in more general situations than already well established hydrodynamics [2], should be considered: e.g., a generalized chemical potential µ(ξ) related to a kinetic description (as already pointed out in reference [9]); also the relevance of the state parameters related to the energy dispersion, first pointed out in other context [10] by Ingarden, should be further investigated. The way in which the parameters ζ(t) and the additional preparation parameters determine the statistical operator is the main point in this paper: one has the indication that the concrete feature of the preparation procedure can be represented inside the formalism; so we expect that the concept of suitable preparation procedure should be amenable to experimental text.…”

Section: Discussionmentioning

confidence: 99%

Description of isolated macroscopic systems inside quantum mechanics

Lanz

Melsheimer

Vacchini

2000

Reports on Mathematical Physics

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For an isolated macrosystem classical state parameters ζ(t) are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval [T, t0] a statistical operator is constructed as a solution of the Liouville von Neumann equation, exhibiting at time t the state parameters ζ(t ′ ), t0 ≤ t ′ ≤ t, and preparation parameters related to times T ≤ t ′ ≤ t0. Relation with Zubarev's non-equilibrium statistical operator is discussed. A mechanism for memory loss is investigated and time evolution by a semigroup is obtained for a restricted set of relevant observables, slowly varying on a suitable time scale.

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Section: Discussionmentioning

confidence: 99%

Description of isolated macroscopic systems inside quantum mechanics

Lanz

Melsheimer

Vacchini

2000

Reports on Mathematical Physics

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“…Although both Jaynes (1957a,b) and, later, Ingarden (1961Ingarden ( ,1963Ingarden ( , 1964Ingarden ( , 1965) make a number of rationalizations for the maximization of entropy, it is not a theorem that can be proven from more fundamental postulates, but rather is a statistical law (Wehrl, 1978). The mathematics and the development of the MEP were discussed by Jaynes (1979) in a review article in 1978.…”

Section: Inference Of the Frequency Distribution Of Sizes Of Clustersmentioning

confidence: 98%

Particle clusters in concentrated suspensions. 2. Information theory and particle clusters

Graham¹,

Steele²

1984

Ind. Eng. Chem. Fund.

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We reconstruct the probability distributions of cluster sizes of uniform spheres in concentrated suspensions subjected to homogeneous shear flow by combining partial experimental information with techniques derived from the Maximum Entropy Principle (MEP) and Information theory. Observations of the clusters of a small fraction of labeled particles are used as constraints in a statistical inference procedure based on the MEP to predict the shape of the cluster size distributions for all spheres. The breadth of the cluster size distributions is inferred by applying a technique derived from information theory to the experimental observations. We find that the average cluster size increases rapidly and nonlinearly as the volume concentration increases. Over the range of our data, the average cluster size decreases slightly and the distributions of cluster sizes become more random as the rate of shear increases.

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“…The existence and uniqueness of this solutions follows from the convexity property of entropy (18). This method is a special case of the general method proposed in [9] [ 101 as an application of the LAGRANQE procedure. The name "temperature" seems be appropriate since it is etymologically connected with the Latin "temperare" (= to abstain, be moderate, mix properly, regulate, govern) having nothing to do with heat or energy.…”

Section: Abk (25)mentioning

confidence: 99%

“…[8] [9] [lo] [ll]) based on the maximum entropy principle of JAYNES [12] [13], there appeared recently an independent paper by R. D. LEVINE [14] with very similar ideas to ours, namely about "patterns of maximal entropy".…”

Section: Introductionmentioning

confidence: 99%

Shape as an Information‐Thermodynamical Concept and the Pattern Recognition Problem

Ingarden

Górniewicz

1990

Mathematische Nachrichten

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Dedicated to the 60" birthday of Prof. A . Uhlmann and to the 50" birthday of Prof. Q. LaPner Abstract. A hierarchical classification of different concepts of shape of compact connected sets in Rn (topological, LIPSHITZ, homotopic, BORSTJE and homological shapes) is given. The most general among them is the homological shape. There is only a countable number of homological shapes for connected compact sets in Rn. In the case n = 2 even the number of different BORSUE shapes for connected compact gets is countable. Giving a probability distribution of shapes we can define a shape entropy, a mean shape and shape fluctuations. This enables a formulation of information thermodynamics of shape and its applications to different field6 (physics -small systems, chemistry, biophysics, pattern recognition). The paper does not develop yet these applications, its aim is to clear the basic notions.

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Information Theory and Thermodynamics of Light Part II. Principles of Information Thermodynamics

Cited by 34 publications

References 20 publications

Description of isolated macroscopic systems inside quantum mechanics

Description of isolated macroscopic systems inside quantum mechanics

Particle clusters in concentrated suspensions. 2. Information theory and particle clusters

Shape as an Information‐Thermodynamical Concept and the Pattern Recognition Problem

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