Majorization and dynamics of continuous distributions
arXiv:1811.11617 · doi:10.3390/e21060590
Abstract
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time, within a continuous dynamics, along with an associated majorized Second Law which implies the standard Second Law of thermodynamics but not viceversa. Moreover, mixing dynamics, generalized Fokker-Planck equations and quantum evolutions are explored as majorized ordered chains along the time evolution, being the stationary states the infimum elements.
References in corpus (19)
- Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
- Strong Majorization Entropic Uncertainty Relations
- Mixing property of triangular billiards
- Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
- A General Nonlinear Fokker-Planck Equation and its Associated Entropy
- Quantum chaos and the double-slit experiment
- Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model
- Avoiding irreversibility: engineering resonant conversions of quantum resources
- Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems
- Quantum information as a non-Kolmogorovian generalization of Shannon's theory
- A hierarchical Bayesian perspective on majorization-minimization for non-convex sparse regression: application to M/EEG source imaging
- Quantum Dynamical Entropies in Discrete Classical Chaos
- Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
- On the classical limit of quantum mechanics, fundamental graininess and chaos: compatibility of chaos with the correspondence principle
- A semiclassical condition for chaos based on Pesin theorem
- A Quantum Version of The Spectral Decomposition Theorem of Dynamical Systems, Quantum Chaos Hierarchy: Ergodic, Mixing and Exact
- Lyapunov exponents and Hamiltonian poles in a non Hermitian dynamics
- Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
- Gaussian ensembles distributions from mixing quantum systems