scholarly journals Entropic dynamics of networks

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Felipe Xavier Costa ◽  
◽  
Pedro Pessoa ◽  
Keyword(s):  
Entropic Dynamics

scholarly journals Quantum Trajectories in Entropic Dynamics

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 25
Author(s):  
Nicholas Carrara
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Equation ◽  
Bohmian Mechanics ◽  
Quantum Trajectories ◽  
Stochastic Mechanics ◽  
Scalar Particles ◽  
Double Slit ◽  
The Continuum ◽  
Entropic Dynamics

Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson’s stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.

scholarly journals Entropic dynamics: reconstructing quantum field theory in curved space-time

2019 ◽  
Vol 36 (20) ◽  
pp. 205013 ◽  
Author(s):  
Selman Ipek ◽  
Mohammad Abedi ◽  
Ariel Caticha
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Entropic Dynamics

scholarly journals Entropic Dynamics in Neural Networks, the Renormalization Group and the Hamilton-Jacobi-Bellman Equation

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 587
Author(s):  
Nestor Caticha
Keyword(s):  
Neural Networks ◽  
Renormalization Group ◽  
Bayesian Learning ◽  
Bellman Equation ◽  
Depth Limit ◽  
Feed Forward ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Continuum ◽  
Entropic Dynamics

We study the dynamics of information processing in the continuum depth limit of deep feed-forward Neural Networks (NN) and find that it can be described in language similar to the Renormalization Group (RG). The association of concepts to patterns by a NN is analogous to the identification of the few variables that characterize the thermodynamic state obtained by the RG from microstates. To see this, we encode the information about the weights of a NN in a Maxent family of distributions. The location hyper-parameters represent the weights estimates. Bayesian learning of a new example determine new constraints on the generators of the family, yielding a new probability distribution which can be seen as an entropic dynamics of learning, yielding a learning dynamics where the hyper-parameters change along the gradient of the evidence. For a feed-forward architecture the evidence can be written recursively from the evidence up to the previous layer convoluted with an aggregation kernel. The continuum limit leads to a diffusion-like PDE analogous to Wilson’s RG but with an aggregation kernel that depends on the weights of the NN, different from those that integrate out ultraviolet degrees of freedom. This can be recast in the language of dynamical programming with an associated Hamilton–Jacobi–Bellman equation for the evidence, where the control is the set of weights of the neural network.

scholarly journals Relational entropic dynamics of particles

2016 ◽  
Author(s):  
Selman Ipek ◽  
Ariel Caticha
Keyword(s):  
Dynamics Of Particles ◽  
Entropic Dynamics

scholarly journals Entropic Dynamics of Exchange Rates and Options

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 586 ◽  
Author(s):  
Mohammad Abedi ◽  
Daniel Bartolomeo
Keyword(s):  
Exchange Rate ◽  
Exchange Rates ◽  
Inductive Inference ◽  
Relevant Information ◽  
Scale Transformation ◽  
European Options ◽  
No Arbitrage ◽  
Model Dynamics ◽  
The Exchange Rate ◽  
Entropic Dynamics

An Entropic Dynamics of exchange rates is laid down to model the dynamics of foreign exchange rates, FX, and European Options on FX. The main objective is to represent an alternative framework to model dynamics. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. Entropic Dynamics is an application of entropic inference, which is equipped with the entropic notion of time to model dynamics. The scale invariance is a symmetry of the dynamics of exchange rates, which is manifested in our formalism. To make the formalism manifestly invariant under this symmetry, we arrive at choosing the logarithm of the exchange rate as the proper variable to model. By taking into account the relevant information about the exchange rates, we derive the Geometric Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under the scale transformation. Securities should be valued such that there is no arbitrage opportunity. To this end, we derive a risk-neutral measure to value European Options on FX. The resulting model is the celebrated Garman–Kohlhagen model.

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