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

Communications in Theoretical Physics

A Framework for Non-Equilibrium Statistical Ensemble Theory

Bi Qiao, Zu-Tan He, Jie Liu

Published Jul 1, 2011• 0 citations
Publisher

Abstract

Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the theory to non-equilibrium domain, however the status of the theory of non-equilibrium phenomena can not be said so well established as the Gibbsian ensemble theory. In this work, we present a formalism for the non-equilibrium statistical ensemble based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.

DOI
10.1088/0253-6102/56/1/19

Related papers

Exploring non-equilibrium statistical ensembles

Bi Qiao, Jie Liu

Since Gibbs synthesized a general equilibrium statistical ensemble theory, generalizing the Gibbsian theory to non-equilibrium phenomena has been a dream for some theorists. However, the status of the theory for the non-equilibrium ensemble formalism is not as well established as the Gibbsian ensemble theory. In this work, we explore the formalism behind the non-equilibrium statistical ensemble theory based on the sub-dynamic kinetic equation originating from the Brussels-Austin school and developed further by others. The key is establishing a similarity transformation between Gibbsian ensembles and the sub-dynamic ensemble. Using this way, we study a spin-Boson model with strong coupling. A reduced density operator for the canonical ensemble can be easily obtained and the relevant decoherence-free property is revealed.

Chinese Science Bulletin•Dec 1, 2011•2 citations

A Framework for Non-Equilibrium and Equilibrium Statistical Ensembles

Fang Jin-Qing

In this paper, we establish a non-equilibrium statistical ensemble formalism through a subdynamic equation.A framework constructed to study the weak or strong interaction in the case of the spin-boson model, so that it is easy to get a reduced density operator for the quantum canonical ensembles. A strongly correlated quantum network based on the Anderson model has also been discussed.

Fuza xitong yu fuzaxing kexue•Jan 1, 2010•0 citations

Constructing non-equilibrium statistical ensemble formalism based on Subdynamics

Bi Qiao

In this work, we present a general non-equilibrium ensemble formalism based on the subdynamic equation (SKE). The constructing procedure is to use a similarity transformation between Gibbsian ensemble formalism and the non-equilibrium ensemble formalism. The obtained density distribution is a projected one that can represent essence part of (irreversible) evolution of the density distribution, by which a generalized reduced density distribution for the quantum canonical ensembles is studied and applications in Cayley tree and spin network are discussed.

arXiv:0709.2116•Sep 13, 2007•0 citations

Non-equilibrium theory of projected ensembles

Fabio Anza, Cameron Hahn

Projected ensembles---the collections of conditional pure states induced on a system by measuring an entangled environment---have become central objects in quantum science, underlying deep thermalization, quantum state designs, the emergence of classicality, and exhibiting interesting phase transitions. Here we develop a general and exact theory of their dynamics, yielding a systematic approach to their dynamics and equilibrium and non-equilibrium stationary states. We derive an exact continuity equation on quantum state space for the projected ensemble, together with microscopic kinetic equations and analytical expressions for the probability flux and source terms generated by the system-environment interaction. The resulting dynamics admits a classical representation: isolated systems obey Hamiltonian transport and Liouville's theorem, while open systems are described by a kinetic theory of probability transport. The stationary continuity equation provides a general characterization of equilibrium and non-equilibrium stationary projected ensembles, which can be analyzed through the method of characteristics. The theory provides an analytical framework for studying the emergence, structure, and timescales of equilibrium and non-equilibrium stationary projected ensembles, with applications ranging from deep thermalization and the emergence of classicality to random quantum-state generation and quantum device benchmarking.

quant-pharXiv:2608.10110•Aug 12, 2026•0 citations

Nonequilibrium Statistical Ensemble Formalism and Quantum Strongly Correlated Network

Fang Jin-Qing

In this work,we present a nonequilibrium ensemble formalism based on the subdynamic kine-tic equation.The constructing procedure is to take a similarity transformation to Gibbsian ensemble formalism.This allows one to obtain subdynamic ensemble formalism for projected density operator.This formalism can be considered as a generalization of the equilibrium quantum canonical ensemble formula in the sense as 1) if the similarity operator is unitary,then the new formula is just an effective representation of the old canonical ensemble formula,2) if the similarity operator is non-unitary,then the new formula is an extension of the old formula,which represents a kind of non-equilibrium quantum canonical ensembles formula and reflects irreversibility of the system,and 3) if the similarity operator can be deduced by some approximations,such as Markovian/non-Markovian approximations,then the new formula can expose some irreversibility characteristics of the system which can not be gained from the equilibrium quantum ensemble formulas.As an application,we study a quantum strongly correlated network described by an Anderson model.A Green function based on this formalism is also introduced.We find the complex entropy of the system to be related to appearance of the local magnetic vectors in the nodes of the network,where the image part of the entropy represents an evolution rate of the entropy.

Fuza xitong yu fuzaxing kexue•Jan 1, 2009•0 citations

Nonequilibrium Phenomena in Strongly Correlated Systems

David Bernhard Blaschke, Alexandra V. Friesen, V. G. Morozov +2 more

The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev's approach, which generalizes the notion of Gibbs' ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev's method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly

MDPI eBooks•Sep 28, 2020•1 citation
Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the theory to non-equilibrium domain, however the status of the theory of non-equilibrium phenomena can not be said so well established as the Gibbsian ensemble theory. In this work, we present a formalism for the non-equilibrium statistical ensemble based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.
Since Gibbs synthesized a general equilibrium statistical ensemble theory, generalizing the Gibbsian theory to non-equilibrium phenomena has been a dream for some theorists. However, the status of the theory for the non-equilibrium ensemble formalism is not as well established as the Gibbsian ensemble theory. In this work, we explore the formalism behind the non-equilibrium statistical ensemble theory based on the sub-dynamic kinetic equation originating from the Brussels-Austin school and developed further by others. The key is establishing a similarity transformation between Gibbsian ensembles and the sub-dynamic ensemble. Using this way, we study a spin-Boson model with strong coupling. A reduced density operator for the canonical ensemble can be easily obtained and the relevant decoherence-free property is revealed.
In this work, we present a general non-equilibrium ensemble formalism based on the subdynamic equation (SKE). The constructing procedure is to use a similarity transformation between Gibbsian ensemble formalism and the non-equilibrium ensemble formalism. The obtained density distribution is a projected one that can represent essence part of (irreversible) evolution of the density distribution, by which a generalized reduced density distribution for the quantum canonical ensembles is studied and applications in Cayley tree and spin network are discussed.
Projected ensembles---the collections of conditional pure states induced on a system by measuring an entangled environment---have become central objects in quantum science, underlying deep thermalization, quantum state designs, the emergence of classicality, and exhibiting interesting phase transitions. Here we develop a general and exact theory of their dynamics, yielding a systematic approach to their dynamics and equilibrium and non-equilibrium stationary states. We derive an exact continuity equation on quantum state space for the projected ensemble, together with microscopic kinetic equations and analytical expressions for the probability flux and source terms generated by the system-environment interaction. The resulting dynamics admits a classical representation: isolated systems obey Hamiltonian transport and Liouville's theorem, while open systems are described by a kinetic theory of probability transport. The stationary continuity equation provides a general characterization of equilibrium and non-equilibrium stationary projected ensembles, which can be analyzed through the method of characteristics. The theory provides an analytical framework for studying the emergence, structure, and timescales of equilibrium and non-equilibrium stationary projected ensembles, with applications ranging from deep thermalization and the emergence of classicality to random quantum-state generation and quantum device benchmarking.
In this work,we present a nonequilibrium ensemble formalism based on the subdynamic kine-tic equation.The constructing procedure is to take a similarity transformation to Gibbsian ensemble formalism.This allows one to obtain subdynamic ensemble formalism for projected density operator.This formalism can be considered as a generalization of the equilibrium quantum canonical ensemble formula in the sense as 1) if the similarity operator is unitary,then the new formula is just an effective representation of the old canonical ensemble formula,2) if the similarity operator is non-unitary,then the new formula is an extension of the old formula,which represents a kind of non-equilibrium quantum canonical ensembles formula and reflects irreversibility of the system,and 3) if the similarity operator can be deduced by some approximations,such as Markovian/non-Markovian approximations,then the new formula can expose some irreversibility characteristics of the system which can not be gained from the equilibrium quantum ensemble formulas.As an application,we study a quantum strongly correlated network described by an Anderson model.A Green function based on this formalism is also introduced.We find the complex entropy of the system to be related to appearance of the local magnetic vectors in the nodes of the network,where the image part of the entropy represents an evolution rate of the entropy.
The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev's approach, which generalizes the notion of Gibbs' ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev's method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly