Recently, as essence of information geometry, Barbaresco has synthetized the analogies between both Koszul and Souriau characteristic function models, and reduced their definitions to the exclusive Cartan Inner Product. Interpreting Legendre transform as Fourier transform in (Min,+) algebra, he concludes with a definition of entropy given by a relation mixing Fourier/Laplace transforms. The computational methods currently used in classic and quantum geometric science of information (GSI) are based on the discretization of differential equations. The purpose of this paper is to arrive to the proposal of a stronger computational point of view. CICT new awareness of a rational hyperbolic geometry framework of coded heterogeneous hyperbolic structures, underlying the familiar Q Euclidean surface representation system, can open the way to holographic information geometry (HIG). This formulation has the great merit of maintaining close contact between the mathematical description and the physical phenomenon described, showing how to obtain a purely algebraic formulation of information and physical laws relating directly elementary information generators to experimental measurements.
CICT holographic information geometry
FIORINI, RODOLFO
2015
Abstract
Recently, as essence of information geometry, Barbaresco has synthetized the analogies between both Koszul and Souriau characteristic function models, and reduced their definitions to the exclusive Cartan Inner Product. Interpreting Legendre transform as Fourier transform in (Min,+) algebra, he concludes with a definition of entropy given by a relation mixing Fourier/Laplace transforms. The computational methods currently used in classic and quantum geometric science of information (GSI) are based on the discretization of differential equations. The purpose of this paper is to arrive to the proposal of a stronger computational point of view. CICT new awareness of a rational hyperbolic geometry framework of coded heterogeneous hyperbolic structures, underlying the familiar Q Euclidean surface representation system, can open the way to holographic information geometry (HIG). This formulation has the great merit of maintaining close contact between the mathematical description and the physical phenomenon described, showing how to obtain a purely algebraic formulation of information and physical laws relating directly elementary information generators to experimental measurements.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
