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

Physica A Statistical Mechanics and its Applications

Maximum entropy, Lie algebras and quantum thermodynamics

H.L. Varela, Angelo Plastino

Published May 1, 1994• 1 citation
Publisher
DOI
10.1016/0378-4371(94)90122-8

Related papers

Maximum Entropy Principle and Quantum Mechanics

Araceli N. Proto

Springer eBooks•Jan 1, 1990•11 citations

Equilibration to the non-Abelian squeezed-thermal reservoir with three charges

S. Shahidani

In quantum thermodynamics, the noncommutativity of conserved quantities is a key aspect of generalized reservoirs. Squeezed-thermal reservoirs, characterized as non-Abelian thermal reservoirs with noncommuting constant quantities (charges), are redefined in this study using SU(1,1) Lie algebra generators. Our findings suggest that these reservoirs can be more accurately described as generalized Gibbs ensembles featuring three noncommuting operators instead of the generally assumed two. By incorporating three charges and the quantum phase-space method to describe dissipation into such a reservoir, two expressions for Wigner entropy production are derived: one based on the stationary mean value of the exchanged charges and another based on a single operator's stationary mean value---the Casimir operator of the Lie algebra. Analysis of these expressions across two distinct models sheds light on equilibration conditions with generalized reservoirs during the interconversion of noncommuting charges.

Physical Review A•Nov 15, 2024•1 citation

Quantum Theory and Statistical Thermodynamics

Peter Hertel

Graduate texts in physics•Jan 1, 2017•1 citation

The maximum entropy principle for radiation fields

Qiao Gu

The maximum entropy principle discovered by Jaynes E T governs a search of the most reasonable probability assignment of stochastic variable,based on the measured data.One of the simplest applications of this principle lies in that all the thermodynamical relations are derived from the maximizing entropy of the system with energy as a single measured value.The maximum entropy principle is used then for the radiation field as a quantum system.Our results show that with an increase of the number of measurable quantities,the thermal field,the coherent states as well as the squeezed states are automatically introduced in turn;in particular,the dependence of all the properties of these radiation fields on the thermal noise is formulated quantitatively.The fundamental results obtained in this paper are expected to provide a basis for applications of the maximum entropy principle in some fields,such as quantum optics,quantum informatics,biophotonics,and related interdisciplinary science.

JOURNAL OF SHENZHEN UNIVERSITY SCIENCE AND ENGINEERING•Jan 1, 2011•1 citation

NOTES ON QUANTUM ENTROPY

Makoto Ohya, D�nes Petz

WORLD SCIENTIFIC eBooks•Feb 1, 2008•2 citations

Compacting the Time Evolution of the Forced Morse Oscillator Using Dynamical Symmetries Derived by an Algebraic Wei-Norman Approach

James Russell Hamilton, F. Remacle, Raphael David Levine

High Resolution Image Download MS PowerPoint Slide A practical approach is put forward for a compact representation of the time evolving density matrix of the forced Morse oscillator. This approach uses the factorized product form of the unitary time evolution operator, à la Wei-Norman. This product form casts the time evolution operator in the basis of operators that form a closed Lie algebra. The further requirement that the Hamiltonian of the system be closed within this Lie algebra is satisfied by restricting the dynamics to its sudden limit. One is thereby able to propagate in time both pure and mixed quantum states. As an example, for a thermal initial state, the time-evolved density matrix of maximum entropy is derived, and it is compacted to be described by only three explicit constraints: one time-dependent constraint, which is a dynamical symmetry, and two constants of the motion, with corresponding time-independent coefficients. This representation is a significant reduction from O ( j 2 ) constraints down to just three, where j is the number of bound states of the Morse oscillator.

Journal of Chemical Theory and Computation•Apr 29, 2025•4 citations
In quantum thermodynamics, the noncommutativity of conserved quantities is a key aspect of generalized reservoirs. Squeezed-thermal reservoirs, characterized as non-Abelian thermal reservoirs with noncommuting constant quantities (charges), are redefined in this study using SU(1,1) Lie algebra generators. Our findings suggest that these reservoirs can be more accurately described as generalized Gibbs ensembles featuring three noncommuting operators instead of the generally assumed two. By incorporating three charges and the quantum phase-space method to describe dissipation into such a reservoir, two expressions for Wigner entropy production are derived: one based on the stationary mean value of the exchanged charges and another based on a single operator's stationary mean value---the Casimir operator of the Lie algebra. Analysis of these expressions across two distinct models sheds light on equilibration conditions with generalized reservoirs during the interconversion of noncommuting charges.
The maximum entropy principle discovered by Jaynes E T governs a search of the most reasonable probability assignment of stochastic variable,based on the measured data.One of the simplest applications of this principle lies in that all the thermodynamical relations are derived from the maximizing entropy of the system with energy as a single measured value.The maximum entropy principle is used then for the radiation field as a quantum system.Our results show that with an increase of the number of measurable quantities,the thermal field,the coherent states as well as the squeezed states are automatically introduced in turn;in particular,the dependence of all the properties of these radiation fields on the thermal noise is formulated quantitatively.The fundamental results obtained in this paper are expected to provide a basis for applications of the maximum entropy principle in some fields,such as quantum optics,quantum informatics,biophotonics,and related interdisciplinary science.
High Resolution Image Download MS PowerPoint Slide A practical approach is put forward for a compact representation of the time evolving density matrix of the forced Morse oscillator. This approach uses the factorized product form of the unitary time evolution operator, à la Wei-Norman. This product form casts the time evolution operator in the basis of operators that form a closed Lie algebra. The further requirement that the Hamiltonian of the system be closed within this Lie algebra is satisfied by restricting the dynamics to its sudden limit. One is thereby able to propagate in time both pure and mixed quantum states. As an example, for a thermal initial state, the time-evolved density matrix of maximum entropy is derived, and it is compacted to be described by only three explicit constraints: one time-dependent constraint, which is a dynamical symmetry, and two constants of the motion, with corresponding time-independent coefficients. This representation is a significant reduction from O ( j 2 ) constraints down to just three, where j is the number of bound states of the Morse oscillator.