Arrow of time

This is reasonable, since the arrow of time is provided by the adiabatic evolution of the subsystem in the intermediate regime. The perturbative influence of the... 

Eigen s theory describes the self-organisation of biological macromolecules on the basis of kinetic considerations and mathematical formulations, which are in turn based on the thermodynamics of irreversible systems. Evolutionary processes are irreversibly linked to the flow of time. Classical thermodynamics alone cannot describe them but must be extended to include irreversible processes, which take account of the arrow of time (see Sect. 9.2). Eigen s theory is based on two vital concepts ... 

He wrote this in 1925. Eliot s poem, in turn, inspired others. In 1927, the astronomer Sir Arthur Eddington said that if entropy was always increasing, then we can know the direction in which time moves by looking at the direction in which it increases. The phrase entropy is the arrow of time gripped the popular imagination, although it is rather meaningless. 

The idea of entropy being the arrow of time has attracted a huge following from mystical poets through to Marxists (see http //www.marxist.com/science/arrowoftime.html). The outline of the science in the Marxist.com site is actually very good. 

The site http //www-groups. dcs. st-and. ac. uk/ history/Mathematicians/Eddington. html contains a brief biography of Sir Arthur Eddington, who first proposed the phrase arrow of time . 

With these definitions, it is very easy to draw the diagram corresponding to a given term of the expansion (41) reading a contribution from right to left (i.e. in the arrow of time), the lines of the initial state p ipl 0) are first represented then each of the interactions which lead the system to the intermediate states k", (k ". .. are indicated by the corresponding elementary vertex of Fig. 3 until the final state k is reached. These vertices are ordered from right to left. 

It is important to stress the fact that in the proof of the MPC theorem, the laws of classical dynamics are never violated. One could summarize the signihcance of the MPC theorem by saying that, for a well-defined class of dynamical systems, the new formulation lays bare the arrow of time that is hidden in the illusorily deterministic formulation of these unstable systems. 

The irreversible processes (associated with the arrow of time) are as real as the reversible processes described by the traditinal laws of physics they cannot be interpreted as approximations of the fundamental laws. 

GEN.201.1. Prigogine, ZeitpfeilundNaturgesetze, Eine neue Deutung der Irreversibilitat vonZeit (The arrow of time and the laws of nature, a new interpretation of time irreversibility), Aus Forschung und Medizin 9, 65-74 (1994). 

GEN.229. I. Prigogine, Zeitpfeil und instabile dynamische Systeme (The arrow of time and dynamically unstable systems), Ziircher Zeit. 1996. 

GEN.233.1. Prigogine, Chasing the arrow of time, On Campus, The University of Texas at Austin, 20/06/96. 

GEN.277.1. Prigogine, The arrow of time, in The chaotic Universe, V. Gurzadyan, ed., Proc. 2-d ICRA Network Workshop, Rome, Pescara, World Scientific, Singapore, 2000. 

Coveney, P. and High field, R. (1991). The Arrow of Time . Ballantyne Books, New York. Cramer, F. (1993). Chaos and Order. The Complex Structure of Living Systems . VCH,... 

The theme of the conference was divided into three parts the first one concerned General Statements of Cosmological Theory. It was introduced by speeches by Lemaitre, on the Primaeval Atom Hypothesis and the Problem of Clusters of Galaxies, by Oscar Klein who developed Some Considerations Regarding the Earlier Development of the System of Galaxies, and by Hoyle on The Steady-State Theory. This was followed by a talk by Gold, on the Arrow of Time and another by Wheeler on Some Implications of General Relativity for the Structure and Evolution of the Universe. ... 

Irreversible processes correspond to the time evolution in which the past and the future play different roles. In processes such as heat conduction, diffusion, and chemical reaction there is an arrow of time. As we have seen, the second law postulates the existence of entropy 5, whose time change can be written as a sum of two parts One is the flow of entropy deS and the other is the entropy production dtS, what Clausius called uncompensated heat, ... 

Self-organization could be considered as a set intersecting self-assembly, ordered self-assembly, that would (1) contain the systems presenting a spontaneous emergence of order in either space or time or both (2) cover spatial (structural) and temporal (dynamic) order of both equilibrium structures and of non-equilibrium, dissipative structures, incorporating non-linear chemical processes, energy flow and the arrow of time (3) concern only the non-covalent, supramolecular level (4) be... 

Let us postulate that we live in a 3D hypersurface that slides along the u axis with speed v°u = ca, where the u axis coincides with the arrow of time. The 4-velocity is then a (row or column) vector 1 a = ( ca,vx,vy,vz). The plus (resp. minus) sign corresponds to the speed of preons that enter (resp. leave) our 3D world, parallel (resp. antiparallel) to the time arrow. It will be seen below that this constant ca is the one that enters Einstein s mass-energy equation, and corresponds to the speed of our 3D world along the time axis (interpretation 2 in Fig. 1). The speed of electromagnetic radiation in free space is a different constant c. The value of the latter may be either identical or numerically close to c , depending of whether one adopts a relativistic or an emission theory for photons, respectively (see Section V). 

Notice that the direction of the process and time have been determined This has been called the arrow of time [2], Time proceeds in the direction of entropy generation, that is, toward a state of greater probability for the total of the system and its environment, which, in the widest sense, makes up the universe. Finally, we wish to point out that an interesting implication of Equation 2.10 is that for substances in the perfect crystalline state at T = 0 K, the thermodynamic probability Q = 1 and thus S = 0. 

Entropy in an isolated system increases dS/dt> 0 until it reaches equilibrium dS/dt = 0, and displays a direction of change leading to the thermodynamic arrow of time. The phenomenological approach favoring the retarded potential over the solution to the Maxwell field equation is called the time arrow of radiation. These two arrows of time lead to the Einstein-Ritz controversy Einstein believed that irreversibility is based on probability considerations, while Ritz believed that an initial condition and thus causality is the basis of irreversibility. Causality and probability may be two aspects of the same principle since the arrow of time has a global nature. 

The term irreversibility has two different uses and has been applied to different arrows of time. Although these arrows are not related, they seem to be connected to the intuitive notion of causality. Mostly, the word irreversibility refers to the direction of the time evolution of a system. Irreversibility is also used to describe noninvariance of the changes with respect to the nonlinear time reversal transformation. For changes that generate space-time symmetry transformations, irreversibility implies the impossibility to create a state that evolves backward in time. Therefore, irreversibility is time asymmetry due to a preferred direction of time evolution. 

Not too many theories have been formulated from this point of view and some of the more interesting cases are at the speculative stage of development. Even so, it is remarkable how some of the most enigmatic of natural phenomena have no convincing explanation apart from broken-symmetry theories. Included are the initiation or nucleation of phase transitions, superconductivity (T4.5.1), the arrow of time (entropy) and the cosmic imbalance between matter and antimatter. The beauty of the world, indeed seems to lie in approximate symmetries. 

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