Saddles in the energy landscape: extensivity and thermodynamic formalism

Abstract

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.

arXiv comment4 pages, 1 figure

References in corpus (10)

• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
• Saddles in the energy landscape probed by supercooled liquids
• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Energy landscape of a Lennard-Jones liquid: Statistics of stationary points
• Statistical Physics of Structural Glasses
• Thermodynamics of supercooled liquids in the inherent structure formalism: a case study
• Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids
• General features of the energy landscape in Lennard-Jones like model liquids
• The Potential Energy Landscape and Mechanisms of Diffusion in Liquids

Cited by in corpus (15)

• The statistics of critical points of Gaussian fields on large-dimensional spaces
• Do Binary Hard Disks Exhibit an Ideal Glass Transition?
• Characterizing the network topology of the energy landscapes of atomic clusters
• Universal law for the vibrational density of states of liquids
• Phase space geometry and reaction dynamics near index two saddles
• Index k saddles and dividing surfaces in phase space, with applications to isomerization dynamics
• Are there localized saddles behind the heterogeneous dynamics of supercooled liquids?
• Topological properties of the mean field phi^4 model
• Linking high and low temperature plasticity in bulk metallic glasses: thermal activation, extreme value statistics and kinetic freezing
• Geometrical properties of the potential energy of the soft-sphere binary mixture
• Linking high and low temperature plasticity in bulk metallic glasses II: use of a log-normal barrier energy distribution and a mean field description of high temperature plasticity
• A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network
• Relationship between Fragility, Diffusive Directions and Energy Barriers in a Supercooled Liquid
• Energy landscape properties studied by symbolic sequences
• The Angell Plot from the Potential Energy Landscape Perspective