Saddles in the energy landscape: extensivity and thermodynamic formalism

Details Saddles in the energy landscape: extensivity and thermodynamic formalism Saddles in the energy landscape: extensivity and thermodynamic formalism

2003-05-28

arxiv.org/abs/cond-mat/0305665v1

Phys. Rev. Lett. 92, 035506 (2004)

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.92.035506

We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system size, as well as several approximations for the properties of low-order saddles (i.e., those with only a few unstable directions). We then cast the canonical partition function in a saddle-explicit form and develop, for the first time, a rigorous energy landscape approach capable of reproducing trends observed in simulations, in particular the temperature dependence of the energy and fractional order of sampled saddles.

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