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Ensemble Method in the Theory of Irreversibility
Abstract
We describe a new formulation of methods introduced in the theory of irreversibility by Van Hove and Prigogine, with the purpose of making their ideas easier to understand and to apply. The main tool in this reformulation is the use of projection operators in the Hilbert space of Gibbsian ensemble densities. Projection operators are used to separate an ensemble density into a ``relevant'' part, needed for the calculation of mean values of specified observables, and the remaining ``irrelevant'' part. The relevant part is shown to satisfy a kinetic equation which is a generalization of Van Hove's ``master equation to general order.'' Diagram summation methods are not used. The formalism is illustrated by a new derivation of the Prigogine-Brout master equation for a classical weakly interacting system.
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Cites
Description of States in Quantum Mechanics by Density Matrix and Operator Techniques
Fano, U. (1957) · Reviews of Modern Physics · doi:10.1103/revmodphys.29.74 · Cited by 1,975
Variational Principles for Scattering Processes. I
Lippmann, B. A., & Schwinger, J. (1950) · Physical Review · doi:10.1103/physrev.79.469 · Cited by 1,308
Quantum-mechanical perturbations giving rise to a statistical transport equation
van Hove, L. (1954) · Physica · doi:10.1016/s0031-8914(54)92646-4 · Cited by 715
Cited by
Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945
Completely positive dynamical semigroups of N -level systems
Gorini, V., Kossakowski, A., & Sudarshan, E. C. G. (1976) · Journal of Mathematical Physics · doi:10.1063/1.522979 · Cited by 3,998
Path integral approach to quantum Brownian motion
Caldeira, A. O., & Leggett, A. J. (1983) · Physica A: Statistical Mechanics and its Applications · doi:10.1016/0378-4371(83)90013-4 · Cited by 2,772
Nonequilibrium dynamical mean-field theory and its applications
Aoki, H., Tsuji, N., Eckstein, M., Kollar, M., Oka, T., & Werner, P. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.779 · Cited by 773
Concepts and Methods in the Theory of Open Quantum Systems
Breuer, H.-P., & Petruccione, F. (2003) · Lecture Notes in Physics · doi:10.1007/3-540-44874-8_4 · Cited by 746
Metadata
- Authors
- Zwanzig, R.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1960-11-01
- Volume
- 33
- Issue
- 5
- Pages
- 1338-1341
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2083590256
- Cited by
- 2,382
- References
- 3
- FWCI
- 4.72
- Type
- journal article
- Language
- en
- Open access
- closed
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