Entropic Dynamics

Caticha, Ariel

doi:10.3390/e17096110

Cited by 49 publications

(51 citation statements)

References 36 publications

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“…As discussed in [2][3][4][5] entropic time is measured by the fluctuations themselves (see eq. (8) below) which leads to the choice…”

Section: Entropic Dynamics -A Brief Overviewmentioning

confidence: 99%

“…Within the family of microscopic models with ξ = 0 we can also take the "Bohmian" limit, α ′ → ∞. Increasing α ′ at fixedη suppresses the fluctuations so the particles follow smoother 5 In the hybrid theory ξ and are independent parameters. ξ is set to 0 and is defined as the constant with the appropriate units of action that is needed to define a wave function Ψ = ρ 1/2 e iΦ/ .…”

Section: Another Universality Class and Its Bohmian Limitmentioning

confidence: 99%

“…First, the two notions of momentum, (24) and (26), are not unrelated. As shown in [5] the infinitesimal displacement of a functional f [ρ, Φ] is given by its Poisson bracket with the "ensemble" momentum…”

Section: Momentum and Its Uncertainty Relationsmentioning

confidence: 99%

“…1 As in any theory of inference, establishing the subject matter is the first and most crucial step; this amounts to a choice of microstates, that is, a choice of beables. Once that choice is made the dynamics is driven by entropy subject to constraints which reflect the information needed for making physical predictions [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class

Bartolomeo

Caticha

2016

J. Phys.: Conf. Ser.

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Abstract. Entropic Dynamics (ED) is a framework that allows the formulation of dynamical theories as an application of entropic methods of inference. In the generic application of ED to derive the Schrödinger equation for N particles the dynamics is a non-dissipative diffusion in which the system follows a "Brownian" trajectory with fluctuations superposed on a smooth drift. We show that there is a family of ED models that differ at the "microscopic" or sub-quantum level in that one can enhance or suppress the fluctuations relative to the drift. Nevertheless, members of this family belong to the same universality class in that they all lead to the same emergent Schrödinger behavior at the "macroscopic" or quantum level. The model in which fluctuations are totally suppressed is of particular interest: the system evolves along the smooth lines of probability flow. Thus ED includes the Bohmian or causal form of quantum mechanics as a special limiting case. We briefly explore a different universality class -a nondissipative dynamics with microscopic fluctuations but no quantum potential. The Bohmian limit of these hybrid models is equivalent to classical mechanics. Finally we show that the Heisenberg uncertainty relation is unaffected either by enhancing or suppressing microscopic fluctuations or by switching off the quantum potential.

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“…As discussed in [2][3][4][5] entropic time is measured by the fluctuations themselves (see eq. (8) below) which leads to the choice…”

Section: Entropic Dynamics -A Brief Overviewmentioning

confidence: 99%

Section: Another Universality Class and Its Bohmian Limitmentioning

confidence: 99%

Section: Momentum and Its Uncertainty Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class

Bartolomeo

Caticha

2016

J. Phys.: Conf. Ser.

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“…In the application of ED to derive the Schrödinger equation for N particles the physical input is introduced through constraints that are implemented using Lagrange multipliers [2]- [5]. There is one set of N constraints, one for each particle, that control the quantum fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Entropic dynamics: The Schrödinger equation and its Bohmian limit

Bartolomeo¹,

Caticha²

2016

AIP Conference Proceedings

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Abstract. In the Entropic Dynamics (ED) derivation of the Schrödinger equation the physical input is introduced through constraints that are implemented using Lagrange multipliers. There is one constraint involving a "drift" potential that correlates the motions of different particles and is ultimately responsible for entanglement. The purpose of this work is to deepen our understanding of the corresponding multiplier α . We find that α must take integer values. Its main effect is to control the strength of the drift relative to the fluctuations. We show that ED exhibits a symmetry: models with different values of α can lead to the same Schrödinger equation; different "microscopic" or sub-quantum models lead to the same "macroscopic" or quantum behavior. In the limit of large α the drift prevails over the fluctuations and the particles tend to move along the smooth probability flow lines. Thus ED includes the causal or Bohmian form of quantum mechanics as a special limiting case.

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Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Caticha

2018

Annalen der Physik

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Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single-valuedness of wave functions.

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Entropic Dynamics

Cited by 49 publications

References 36 publications

Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class

Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class

Entropic dynamics: The Schrödinger equation and its Bohmian limit

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

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