Potential energy fluctuations

Figure 6. The Allan variance of potential energy fluctuations, (a) The original BLN model and (b) the Go-like BLN model.

Figure 8 depicts the power spectra S(f) of the potential energy fluctuations of the original BLN and the Go-like model at the collapse and folding temperatures. 

Figure 9 presents exponents a for both models as a function of temperature. The Go-like model exhibits a much sharper transition to a white noise spectrum than the BLN model as the temperature departs from the transition temperature. This finding also mirrors the results obtained from the Allan variance where the Go-model exhibits a sharp transition to nonstationarity around the transition temperature, while this transition is diffuse in the case of the BLN model. It was also shown [64,65] in a two-state-like helix-coil transition of a helical polypeptide that a 1//-noise structure of the potential energy fluctuations... 

We wish to thank Professors R. Stephen Berry, Mikito Toda, M. Sasai, A. Kidera, and A. Kitao for their continuous, insightful discussions and criticisms. We acknowledge Dr. Konstantin S. Rostov for his valuable contribution, especially in the 1 // power spectra analysis of potential energy fluctuations of Brownian Dynamics. We also thank Mr. Gareth Rylance for his critical reading of this manuscript. 

Figure 15. The total potential energy fluctuation for the case (left) where rotational motions are suppressed, and the case (right) where the translational motions are suppressed. The simulation was performed for 64 water molecules with TIPS potential. The temperature is 298 K. [Reprinted with permission from Chem. Rev. 93, 2545-2566 (1993). Copyright 1993 by American Chemical Society.]...

One way to see that a transition is discontinuous is to detect a coexistence of two phases, in this case the orientationally ordered and disordered phases, in a temperature interval. This is revealed by time variation of the potential energy of the cluster. In the temperamre region of phase coexistence, each cluster dynamically transforms between the phases, and its potential energy fluctuates around two different mean values (Fig. 4). In an ensemble of clusters, the coexistence of different phases is observable insofar as a fraction of the clusters (e.g., in a beam [17]) can exhibit the structure of one phase, while another fraction takes on the stmcture of another phase. 

The supercooled liquid catastrophe, if it exists, would necessarily be associated with diverging fluctuations in the structural order parameter F. This stems from the fact that the Y surface develops a vanishing curvature in the F direction as this endpoint is approached. Because the bicyclic octamer elements are bulky, fluctuations in their coiKentration amount to density fluctuations. Diverging density fluctuations then imply diverging isothermal compressibility. Furthermore the infinite slope of the metastable liquid locus at its endpoint implies the divergence of thermal expansion. Potential energy fluctuations remain essentially normal, so constant-volume heat capacity remains small. But the volumetric divergence creates an unbounded constant-pressure heat capacity. 

In the simplest version of MD, the Newton (21) or Lagrange equations (22) are integrated for a closed system, in which the volume, total energy, and number of particles are conserved. This simulates the microcanonical, NVE ensemble. Both kinetic and potential energies fluctuate in the microcanonical ensemble but their sum remains constant. 

Standard molecular dynamics simulations simulate the microcanonical ensemble and, with a constant Hamiltonian, the kinetic and potential energies fluctuate with opposite signs (Fig. 16.2). 

---