Microcanonical temperature

V. Microcanonical Temperature and an Arrhenius Relation with the Lifetime of Isomers... 

D. An Exponential Relation Between the Microcanonical Temperature and Average Lifetimes... 

It turns out that the average lifetime, the key quantity to characterize the isomerization dynamics of a liquid-droplet cluster, satisfies an Arrhenius-like exponential law with what we call microcanonical temperature (Section V). This quantity has been introduced to characterize a variational structure of a... 

V. MICROCANONICAL TEMPERATURE AND AN ARRHENIUS RELATION WITH THE LIFETIME OF ISOMERS... 

Since we have confirmed that the phase space volume can be practically calculated as above (see Appendix B for an illustrated example of such a numerical example), we now make use of it to define a microcanonical temperature. A useful alternative definition of Vst( ) is a convolution type... 

These quantities are anticipated to be suitable for describing dynamics separately in the individual basins. The stair-like variation of the kinetic energy in Ari3, and so on (Fig. 11), has now been idealized to be a statistical quantity as the local microcanonical temperatures. 

It is quite natural to try to plot log(f)fl versus 1/7 ,1, 1. Figure 13 displays a very clear numerical fact An Arrhenius-like exponential relation is observed between the local microcanonical temperature and the inverse of the average lifetime in each basin. Here we have used the numerical data studied in Refs. 8 and 19. The local microcanonical temperatures in Fig. 13 (and Fig. 14) cover the range of the total energy [— 13.5e, —11.0e]. 13.5e is close to the lowest end of the liquid-like... 

Figure 13. Plots of In 1/(t)a versus 1 An Arrhenius relation between the inverse of the lifetimes ((t)a) of the four isomers and their associated local microcanonical temperatures (T ). (Reproduced from Ref. 11 with permission.)...

Defining the microcanonical temperature as a kinetic energy that maximizes a phase-space distribution when projected onto the potential energy coordinate, we have shown that this temperature can characterize a time scale of structural isomerization dynamics in the liquid-like phase. In particular, it has been found that the local microcanonical temperature bears an Arrhenius-like relation to the inverse of the average lifetime in isomerization of M7 clusters. Thus, with this temperature one can extract critical information hidden behind the stepwise fluctuation of the kinetic energy of a trajectory in an isomerization process [33]. We have explored a possible origin of the Arrhenius-like relation. 

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