Nonequilibrium thermodynamics and Fisher information: Sound wave propagation in a dilute gas

Flego, Silvana; Frieden, B. Roy; Plastino, A.; Soffer, B. H.

doi:10.1103/physreve.68.016105

Cited by 48 publications

(53 citation statements)

References 23 publications

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“…Frieden and Soffer advanced some time ago [1,5] the idea of a "Fisher temperature" T F that would play for FIM an identical role as the usual T plays with with regards to the GBS S [3]. This idea was validated later on in a series of papers, by demonstrating that thermodynamics' Legendre structure is exactly reproduced by using I instead of S [4,[6][7][8]. One thus obtains a "Fisher thermodynamics" that is equivalent to the orthodox one.…”

Section: Introductionmentioning

confidence: 86%

“…As stated above, thermodynamics' Legendre structure arises from extremizing I with adequate constraints [4,[6][7][8]. We use the same A i with different Lagrange multipliers.…”

Section: Fisher Information's Relations In Phase Spacementioning

confidence: 99%

“…One thus obtains a "Fisher thermodynamics" that is equivalent to the orthodox one. One just replaces S by I [4,[6][7][8]. We have thus two conjugate pairs: (S, T) and (I, T F ).…”

Section: Introductionmentioning

confidence: 99%

“…We have thus two conjugate pairs: (S, T) and (I, T F ). Instead of (1/T) = dS/dU (U ≡ mean energy) [3], one has (1/T F ) = dI/dU [4,[6][7][8]. A question naturally emerges what kind of thermometer is to be used for T F ?…”

Section: Introductionmentioning

confidence: 99%

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The Fisher Thermodynamics of Quasi-Probabilities

Pennini

Plastino

2015

Entropy

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Abstract:With reference to Lee's treatment of quasi-probabilities, it is seen that the three phase space quasi-probabilities, known as the P-, Husimi and Wigner ones, plus other intermediate ones, generate a common, single Fisher thermodynamics, along the lines developed by Frieden et al. We explore some facets of such thermodynamics and encounter complementarity between two different kinds of Fisher information.

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Section: Introductionmentioning

confidence: 86%

“…As stated above, thermodynamics' Legendre structure arises from extremizing I with adequate constraints [4,[6][7][8]. We use the same A i with different Lagrange multipliers.…”

Section: Fisher Information's Relations In Phase Spacementioning

confidence: 99%

“…One thus obtains a "Fisher thermodynamics" that is equivalent to the orthodox one. One just replaces S by I [4,[6][7][8]. We have thus two conjugate pairs: (S, T) and (I, T F ).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Fisher Thermodynamics of Quasi-Probabilities

Pennini

Plastino

2015

Entropy

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“…1 to describe nonequilibrium phenomena in physics [29,30,31]. It is with these modes that the modal structure of the yield curve follows directly from the Fisher information structure of the yield curve (cf.…”

mentioning

confidence: 99%

Ab initio yield curve dynamics

2005

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We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success of the Nelson Siegel approach to fitting static yield curves and the empirically observed modal structure of yield curves. A practical numerical implementation of this equation of motion is found by using the Karhunen-Lòeve expansion and Galerkin's method to formulate a reduced-order model of yield curve dynamics.Key words: Bond, interest rate, dynamics, Fisher information, yield curve, term structure, principal-component analysis, proper orthogonal decomposition, Karhunen-Lòeve, Galerkin, Fokker-Planck. PACS: 89.65. Gh, 89.70.+c Yield curves are remarkable in that the fluctuations of these structures can be explained largely by a few modes and that the shape of these modes is largely independent of the market of origin: a combination of parsimony and explanatory power rarely seen in financial economics. While these modes play a fundamental role in fixed-income analysis and risk management, both the origin of this modal structure and the relationship between this modal structure and a formal description of yield curve dynamics remain unclear. The purpose of this letter is to show that this modal structure is a natural consequence of the information structure of the yield curve and that this information structure, in turn, implies an equation of motion for yield curve dynamics.1 We thank Prof. Ewan Wright for helpful discussions and encouragement.

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Comparative analysis of information measures of the Dirichlet and Neumann two‐dimensional quantum dots

Olendski

2020

Int J of Quantum Chemistry

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d-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schrödinger equation in position space and the Fourier transform of the corresponding wave function leads to the analytic form of its momentum counterpart too. This paves the way to an efficient computation in either space of Shannon, Rényi and Tsallis entropies, Onicescu energies and Fisher informations; for example, for the latter measure, some particular orbitals exhibit simple expressions in either space at any BC type. A comparative study of the influence of the edge requirement on the quantum information measures proves that the lower threshold of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where one-parameter momentum entropies exist is equal to d/(d + 3) for the Dirichlet hyperball and d/(d + 1) for the Neumann one what means that at the unrestricted growth of the dimensionality both measures have their Shannon fellow as the lower verge. Simultaneously, this imposes the restriction on the upper value of the interval [1/2, α R ) inside which the Rényi uncertainty relation for the sum of the position R ρ (α) and wave vector R γ α 2α−1 components is defined: α R is equal to d/(d − 3) for the Dirichlet geometry and to d/(d − 1) for the Neumann BC. Some other properties are discussed from mathematical and physical points of view. Parallels are drawn to the corresponding properties of the hydrogen atom and similarities and differences are explained based on the analysis of the associated wave functions.

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Nonequilibrium thermodynamics and Fisher information: Sound wave propagation in a dilute gas

Cited by 48 publications

References 23 publications

The Fisher Thermodynamics of Quasi-Probabilities

The Fisher Thermodynamics of Quasi-Probabilities

Ab initio yield curve dynamics

Comparative analysis of information measures of the Dirichlet and Neumann two‐dimensional quantum dots

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