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On a class of equilibrium states under the Kubo-Martin-Schwinger boundary condition

F. Rocca, M. Sirugue, D. Testard

Communications in Mathematical PhysicsDec 1, 196939 citations

On a class of equilibrium states under the Kubo-Martin-Schwinger condition

F. Rocca, M. Sirugue, D. Testard

Communications in Mathematical PhysicsJun 1, 197042 citations

Kubo-Martin-Schwinger states of classical dynamical systems with infinite phase space

A. A. Arsen’ev

Theoretical and Mathematical PhysicsMar 1, 19792 citations

Uniqueness of states satisfying Kubo-Martin-Schwinger boundary conditions in the case of one-dimensional quantum spin systems with finite-range potential

Vadim V. Anshelevich

Theoretical and Mathematical PhysicsOct 1, 19722 citations

Non-Equilibrium Phase Transitions in Cooperative Atomic Systems (Nonlinear Nonequilibrium Statistical Mechanics--Proceedings of the 1978 Oji Seminar at Kyoto,July 10～14,1978)

Daniel F. Walls

Progress of Theoretical PhysicsJan 1, 19780 citations

On the Kubo-Martin-Schwinger Boundary Condition

Huzihiro Araki

The Kubo-Martin-Schwinger boundary condition, which had first been introduced as a property characterizing the canonical ensemble average in quantum statistical mechanics, was later recoginized as a property characterizing the modular automorphisms in the so-called Tomita-Takesaki theory of von Neumann algebras. This miraculous link made it possible to apply powerful mathematical technique supplied by the Tomita-Takesaki theory to a study of some problems in mathematical formulation of statistical mechanics. More recently, the KMS condition in classical statistical mechanics has also been investigated. The aim of this exposition is to review for non-specialists those development of the “rigorous” treatment of statistical mechanics which are related to the KMS condition.The Kubo-Martin-Schwinger boundary condition, which had first been introduced as a property characterizing the canonical ensemble average in quantum statistical mechanics, was later recoginized as a property characterizing the modular automorphisms in the so-called Tomita-Takesaki theory of von Neumann algebras. This miraculous link made it possible to apply powerful mathematical technique supplied by the Tomita-Takesaki theory to a study of some problems in mathematical formulation of statistical mechanics. More recently, the KMS condition in classical statistical mechanics has also been investigated. The aim of this exposition is to review for non-specialists those development of the “rigorous” treatment of statistical mechanics which are related to the KMS condition.

Progress of Theoretical Physics SupplementJan 1, 19784 citations

On the Kubo-Martin-Schwinger Boundary Condition (Nonlinear Nonequilibrium Statistical Mechanics--Proceedings of the 1978 Oji Seminar at Kyoto,July 10～14,1978)

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On the Kubo-Martin-Schwinger Boundary Condition (Nonlinear Nonequilibrium Statistical Mechanics--Proceedings of the 1978 Oji Seminar at Kyoto,July 10～14,1978)

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