Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Liouville Dynamics and the Conservation of Classical Information

Angel Ricardo Plastino, Andreas Daffertshofer

Published Sep 20, 2004• 22 citations
Publisher

Abstract

We show that the invariance of entropic distances under Liouville dynamics yields classical analogues of information-related, quantum mechanical impossible operations. By recourse to Fisher's information measure, we also establish a connection between such classically forbidden operations and statistical estimation theory.
DOI
10.1103/physrevlett.93.138701

Related papers

Liouville Equation, Entropic Distances, and Classical Universal Information Processes

Angel Ricardo Plastino

We consider the possibility of performing, in the context of Liouville dynamics, certain information related, universal processes on classical ensemble probability distributions. This problem constitutes a classical counterpart of the study of universal processes in quantum mechanics, which is nowadays the focus of intensive research. The time independence of appropriate entropic distances between time dependent solutions of Liouville equation allows to establish the impossibility of some of the alluded processes. The present problem is also considered within the framework of discrete classical dynamics.

Progress of Theoretical Physics Supplement•Jan 1, 2006•4 citations

Characterization of Quantum Entangled States and Information Measures

Josep Batle-Vallespir

The present Thesis covers the subject of the characterization of entangled states by recourse to entropic measures, as well as the description of entanglement related to several issues in quantum mechanics, such as the speed of a quantum evolution or the connections existing between quantum entanglement and quantum phase transitions.

arXiv:quant-ph/0603124•Mar 14, 2006•1 citation

Characterization of quantum entangled states and information measure

Josep Batle-Vallespir

The present Thesis covers the subject of the characterization of entangled states by recourse to entropic measures, as well as the description of entanglement related to several issues in quantum mechanics, such as the speed of a quantum evolution or the connections existing between quantum entanglement and quantum phase transitions.

•Mar 14, 2006•2 citations

The Fisher's information and quantum-classical field theory: classical statistics similarity

Jacek Syska

The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed.

arXiv:0811.3600•Nov 21, 2008•2 citations

A new look at the quantum Liouville theorem

Pui Tak Leung

We clarify certain confusions in the literature of the density operator in quantum mechanics, and demonstrate that the quantum Liouville theorem has the same form in both the Schrodinger and the Heisenberg pictures.Our starting point is to treat the density operator as an observable which has its specific time dependence in each of the two pictures.It is further shown that such a formulation will provide the exact correspondence between classical and quantum statistical mechanics with the Liouville theorem being interpreted as a conservation law, which is derivable from the equation of motion only in the quantum case.

•Aug 8, 2020•0 citations

Liouville's Theorem in Classical Mechanics and the Global Information Field

Solov'ev, E.A.

The connection between the concept of a 'Lagrangian manifold' and Liouville’s theorem in classical mechanics and the concept of a global information field in quantum physics is discussed.

Journal of Physical Mathematics•Jan 1, 2015•0 citations
We consider the possibility of performing, in the context of Liouville dynamics, certain information related, universal processes on classical ensemble probability distributions. This problem constitutes a classical counterpart of the study of universal processes in quantum mechanics, which is nowadays the focus of intensive research. The time independence of appropriate entropic distances between time dependent solutions of Liouville equation allows to establish the impossibility of some of the alluded processes. The present problem is also considered within the framework of discrete classical dynamics.
We clarify certain confusions in the literature of the density operator in quantum mechanics, and demonstrate that the quantum Liouville theorem has the same form in both the Schrodinger and the Heisenberg pictures.Our starting point is to treat the density operator as an observable which has its specific time dependence in each of the two pictures.It is further shown that such a formulation will provide the exact correspondence between classical and quantum statistical mechanics with the Liouville theorem being interpreted as a conservation law, which is derivable from the equation of motion only in the quantum case.