The behavior of matter under nonequilibrium conditions: Fundamental aspects and applications. Final report, April 15, 1991--July 14, 1994

Technical Report · Sat Dec 31 04:00:00 EST 1994

DOI:https://doi.org/10.2172/674882· OSTI ID:674882

The authors have introduced an extended formulation of dynamics which allows a clear distinction between temporal behavior of stable systems on one hand, chaotic and unstable systems on the other. For stable systems, the evolution is deterministic and time reversible. For chaotic and unstable systems it is probabilistic and breaks time-symmetry. The new formulation of dynamics incorporates the second law of thermodynamics and leads therefore to a great unification of physics. More precisely: (1) the authors found that unstable dynamical systems have new spectral decompositions in extended functional spaces. These spectral decompositions incorporate new characteristics of the time evolution associated with irreversibility; (2) these new spectral decompositions can be in general obtained iteratively through a well-defined algorithm; and (3) the method provides spectral decompositions of the time evolutions operator in the Liouville space of density matrices or distribution functions which cannot be implemented in the Hilbert space (wave functions) or by trajectories. In summary, they obtain an extension of classical and quantum mechanics. This extension leads to the inclusion of irreversibility into the framework of dynamics. Moreover, it also provides the theoretical basis for probabilistic predictions and control methods for complex systems, where the conventional deterministic predictions and control methods do not work.

• Research Organization: Univ. of Texas, Austin, TX (United States)
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States)
• DOE Contract Number: FG05-88ER13897
• OSTI ID: 674882
• Report Number(s): DOE/ER/13897--T1; ON: DE99001089
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CLASSICAL MECHANICS
DYNAMICS
EIGENVALUES
IRREVERSIBLE PROCESSES
MANY-BODY PROBLEM
MATHEMATICAL SPACE
PROGRESS REPORT
QUANTUM MECHANICS
RANDOMNESS
RESEARCH PROGRAMS
SCATTERING