Fisher info and thermodynamics’ first law

Plastino, A.; Soffer, B. H.

doi:10.1016/j.physa.2006.04.111

Cited by 12 publications

(11 citation statements)

References 21 publications

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“…In this sense our work is complementary to recent efforts due to Esquivel and coworkers [62], Plastino et al [63], Angulo and coworkers [58,64], and Sen and coworkers for constrained Coulomb [65] and spherically symmetric confined hydrogenic [66] systems and various central potentials of Hulthen, Yukawa [67,68] and power [69] types, and other authors for Morse [70], Pö schl-Teller [70,71], and power-type [72] potentials as well as for circular membranes [73]. Now, the door is open for the computation of other information-theoretic measures (e.g., entropic moments, Renyi and Tsallis entropies) and complexity measures.…”

Section: Conclusion and Open Problemssupporting

confidence: 73%

Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states

Dehesa

López-Rosa

Martínez–Finkelshtein

et al. 2009

Int. J. Quantum Chem.

151

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ABSTRACT:The analytic information theory of quantum systems includes the exact determination of their spatial extension or multidimensional spreading in both position and momentum spaces by means of the familiar variance and its generalization, the power and logarithmic moments, and, more appropriately, the Shannon entropy and the Fisher information. These complementary uncertainty measures have a global or local character, respectively, because they are power-like (variance, moments), logarithmic (Shannon) and gradient (Fisher) functionals of the corresponding probability distribution. Here we explicitly discuss all these spreading measures (and their associated uncertainty relations) in both position and momentum for the main prototype in D-dimensional physics, the hydrogenic system, directly in terms of the dimensionality and the hyperquantum numbers which characterize the involved states. Then, we analyze in detail such measures for s-states, circular states (i.e., single-electron states of highest angular momenta allowed within an electronic manifold characterized by a given principal hyperquantum number), and Rydberg states (i.e., states with large radial hyperquantum numbers n).

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Section: Conclusion and Open Problemssupporting

confidence: 73%

Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states

Dehesa

López-Rosa

Martínez–Finkelshtein

et al. 2009

Int. J. Quantum Chem.

151

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“…To avoid such drawbacks and since the quantum probability densities of the potential’s bound states are strongly oscillating, except for a few ones such as e.g., the S states, the entropy-like measures are much more natural and appropriate to quantify the position-momentum uncertainty of the system. In addition these measures (i) characterize numerous fundamental and measurable quantities of physical systems [ 34 ], (ii) are cornerstones of two alternative formulations to classical thermodynamics [ 35 , 36 ], and (iii) are basic variables of the classical and quantum information theory and quantum technologies [ 37 , 38 ] since they quantify the classical and quantum information contents as well as the states’ quantum entanglement.…”

Section: Introductionmentioning

confidence: 99%

Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials

Dehesa

2021

Entropy

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The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, R\'enyi) of position and momentum probability densities. Since the potential is assumed to be analytically unknown, these dispersion and information-theoretical measures are given by means of inequality-type relations which are explicitly shown to depend on dimensionality and state's angular hyperquantum numbers. The spherical-symmetry and spin effects on these spreading properties are obtained by use of various integral inequalities (Daubechies--Thakkar, Lieb--Thirring, Redheffer--Weyl, ...) and a variational approach based on the extremization of entropy-like measures. Emphasis is placed on the uncertainty relations, upon which the essential reason of the probabilistic theory of quantum systems relies.

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“…Moreover, the Fisher information is the basic variable of the principle of extreme physical information [16,[23][24][25][26] which has been used to obtain various fundamental equations of motion in physics [16,26]. It is also being used to rederive classical thermodynamics without the usual concept of Boltzmann's entropy [27,28].…”

Section: Introductionmentioning

confidence: 99%

The Fisher-information-based uncertainty relation, Cramer–Rao inequality and kinetic energy for theD-dimensional central problem

Dehesa¹,

González‐Férez²,

Sánchez-Moreno³

2007

J. Phys. A: Math. Theor.

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The inequality p 2 L + 1 2 2 r −2 , with L being the grand orbital quantum number, and its conjugate relation for (r 2 , p −2) are shown to be fulfilled in the D-dimensional central problem. Their use has allowed us to improve the Fisher-information-based uncertainty relation (I ρ I γ const) and the Cramer-Rao inequalities (r 2 I ρ D 2 ; p 2 I γ D 2). In addition, the kinetic energy and the radial expectation value r 2 are shown to be bounded from below by the Fisher information in position and momentum spaces, denoted by I ρ and I γ , respectively.

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Fisher info and thermodynamics’ first law

Cited by 12 publications

References 21 publications

Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states

Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states

Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials

The Fisher-information-based uncertainty relation, Cramer–Rao inequality and kinetic energy for theD-dimensional central problem

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