Ergodic motion

If this would be so, each state u would be an invariant of motion (the probability of the configuration w 2 would be independent of time) and the system would not be ergodic. The very existence of spontaneous emission shows that this is not so. The system evolves toward thermodynamic equilibrium. 

The basic difference between free fields and interacting fields would be of the same order as between a small (reversible) mechanical system and ergodic dissipative systems. But this means that physical states can no longer be associated with invariants of motion which no longer exist. This leads to deep changes in the structure of the theory. 

Molecular dynamics is frequently portrayed as a method based on the ergodicity hypothesis which states that the trajectory of a system propagating in time through the phase space following the Newtonian laws of motion given by the equations ... 

In conclusion, it is worth reflecting on a classical trajectory study of neutral ethane [335] in which it was found that there were dynamical restrictions to intramolecular energy transfer among C—H motions and between these and C—C motions. It was pointed out [335] that this non-ergodicity might not produce results observable at present levels of experimental resolution. This is probably the situation in mass spectrometry. QET is a respected theory in mass spectrometry because, proceeding from clearly stated assumptions, it is mathematically tractable and is able to explain the currently available experimental data. 

The single, undisturbed motion of the system, if pm-sued without limit in time, will finally traverse every phase point which is compatible with its given total energy. A mechanical system satisfying this condition is called by Boltzmann an ergodic system. "... 

For an ergodic system all motions with the same total energy take place on the same (7-path.M... 

Brownian motion must be taken into account for suspensions of small (submicron-sized) particles. By their very nature, such stochastic Brownian forces favor the ergodicity of any configurational state. Although no completely general framework for the inclusion of Brownian motion will be presented here, its effects will be incorporated within specific contexts. Especially relevant, in the present rheological context, is the recent review by Felderhof (1988) of the contribution of Brownian motion to the viscosity of suspensions of spherical particles. 

In the derivation of the ES FR, time-reversibility of the equations of motion is required. Thus time reversibility is a sufficient condition for the ES FR. The question arises as to whether time reversibility is a necessary condition. In numerical calculations where irreversibility was introduced by employing an applied field that had no definite parity under time reversal, it was difficult to observe the breakdown of the ES FR. Careful numerical experiments have finally shown that a breakdown indeed occurs and identifies how this comes about. This work confirms that time reversibility and ergodic consistency are necessary and sufficient conditions for ES FR. 

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