Time symmetry breaking

MSN. 145. T. Petrosky and I. Prigogine, Quantum chaos, complex spectral representations and time symmetry breaking, Chaos, Solitons and Fractals 4, 311-359 (1994). 

MSN. 159. 1. Prigogine and T. Petrosky, Chaos, time symmetry breaking and the extension of classical and quantum mechanics, in Proceedings, El Escorial course on Foundations of Quantum Physics, Ed. Complutense, Madrid, pp. 183-215. 

MSN. 170.1. Prigogine, Eaws of Nature, Probability and time symmetry breaking, Physica Aid, 528-539 (1999). 

MSN.171.1. Prigogine and T. Petrosky, Laws of nature, probability and time symmetry breaking, in Generalized Functions, Operator Theory and Dynamical Systems, I. Antoniou and G. Lumer, eds.. Chapman Hall, London, pp. 99-110, 1999. 

MSN. 172.1. Prigogine and I. Antoniou, Laws of nature and time symmetry breaking, in Tempos in Science and Nature Structures, Relations and Complexity, Ann. New York Acad. Sci. 879, 8—28 (1999). 

MSN.196. 1. Prigogine, S. Kim, G. Ordonez, and T. Petrosky, Stochasticity and time symmetry breaking in Hamiltonian dynamics, in Proceedings, XXII Solvay Conference Physics, The Physics of Communication, Delphi, 2001, World Scientific, Singapore, 2003, pp. 1-22. 

GEN.287. 1. Prigogine, Dynamical roots of time symmetry breaking, Philos. Trans. Roy. Soc. London, A 360, 299-301 (2002). 

GEN.295.1. Prigogine, Dynamical roots of the time symmetry breaking, in Advanced Topics in Theoretical Chemical Physics, 3-6, J. Maruani et al., eds., 2003, Kluwer, Dordrecht, pp. 3-6. 

The 19th century left us with a conflicting heritage. Classical mechanics and even quantum mechanics and relativity are time-symmetrical theories. The past and the future play the same role in them. On the other hand, thermodynamics introduces entropy, and entropy is associated to the arrow of time. So we have two descriptions of nature. Simplifying somewhat, we may say that the first emphasizes being and the second becoming. This leads to many questions. What is the role of entropy and of distance to equilibrium in nature And a second question is, how does the time-symmetry breaking of entropy relate to the laws of physics ... 

PRIGOGINE I., KIM S., ORDONEZ G. and PETROSKY T., Stochasticity and time-symmetry breaking in Hamiltonian dynamics, proceedings of the XXIInd Solvay Conference of Physics The physics of communication , in Advances in Chemical Physics (to appear). 

Upon involving two or even more variables in connection with spatially inhomogeneous systems, the higher-order non-linearity gives rise to more complex phenomena. The best examples are systems controlled by simultaneous chemical reactions and mass diffusion. From the mathematical point of view, the system becomes localized at the thermodynamic branch and the initially stable solution of the appropriate balance equation bifurcates and new stable solutions suddenly appear often overlapping. One such a possibility is time-symmetry breaking, associated with the merging of time-periodic solutions known as limit... 

The theories that should feature prominently in the understanding of chemical effects have been summarized in this volume, without demonstrating their application. The way forward has been indicated by Primas [67] and in the second volume of this work the practical use of modern concepts such as spontaneous symmetry breaking, non-local interaction, bohmian mechanics, number theories and space-time topology, to elucidate chemical effects will be explored. The aim is to stimulate renewed theoretical interest in chemistry. 

Building on an early theoretical scheme by Frank [16] (see below) for the spontaneous autocatalytic symmetry breaking in which enantiomers act as catalysts for their own production, Kondepudi and Nelson [17-20] further suggested a generalized scheme by which the minor excess of one enantiomer, caused by PVED, might lead to a state of enantiomeric homogeneity. They then calculated that a period as short as 15 000 years could cause chiral domination. [19] In 1989 MacDermott and Tranter [21] maintained that this amplification time would be reduced from 104 years to just one year if the PVED were increased to 10-16 kT , i.e., by a factor of only ten. 

The year 1967 appears as a crucial year In an important paper by Prigogine and Nicohs, On symmetry-breaking instabilities in dissipative systems (TNC.16), there appears for the first time the term dissipative stmctures. The filiation of this concept with the half-principle of Glansdorff and Prigogine can be clearly perceived in the works of that period (particularly in the paper TNG.17). However, the new approach required a radical change of the theoretical methods. 

MSN. 176. T. Petrosky and I. Prigogine, Thermodynamic limit, Hilbert space and breaking of time symmetry, Chaos, SoUtons and Fractals 11, 373—382 (2000). 

PoIIicott-Ruelle Resonances and Time-Reversal Symmetry Breaking Microscopic Construction of the Diffusive Modes... 

IV. POLLICOTT-RUELLE RESONANCES AND TIME-REVERSAL SYMMETRY BREAKING... 

In contrast to the integrable case, the master equation contains the dissipative terms proportional to y, in addition to the free-motion term. These terms break time symmetry and introduce diffusion, which causes the collapse of wave functions. 

Boltzmann s W-function is not monotonic after we perform a velocity inversion of every particle—that is, if we perform time inversion. In contrast, our -function is always monotonic as long as the system is isolated. When a velocity inversion is performed, the 7f-function jumps discontinuously due to the flow of entropy from outside. After this, the 7f-function continues its monotonic decrease [10]. Our -function breaks time symmetry, because At itself breaks time symmetry. 

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