Contact-number fluctuations

The contact numbers and can be considered as system parameters appropriately describing the state of the system and are therefore useful to identify the pseudophases. Peaks and dips in the external-parameter dependence of self-correlations ( j)c, n )c and cross-correlations nsn )c indicate activity in the contact-number fluctuations and, analyzing the expectation values (%) and ( ) in these active regions of the external parameters T and s, allow for an interpretation of the respective conformational transitions between the structural phases. 

In very poor solvent (i.e., for very large values of s), the DC phase may degenerate, at least for flexible finite-length polymers, into separate globular and crystalline subphases (see the discussion in Section 5 and, e.g., in Refs. [127,128,137]). 

In Chapter 4, it has already been stated that it is an advantage of the simple-sampling algorithms based on Rosenbluth sampling [33], compared to importance-sampling methods, that they allow for the approximation of the degeneracy ( density ) of states absolutely, i.e., free energy and entropy can be explicitly determined. 

Expectation values, self- and cross-correlations of the contact numbers n and Om as functions of the temperature T in comparison with the heat capacity for a 179-mer in solvent with s = 1. From [302]. 

This example shows that a study of the contact number fluctuations is indeed sufficient to qualitatively identify and describe the conformational transitions between the pseudophases of the hybrid system. For this reason, % and are adequate system parameters, which play a similar role like order parameters in thermodynamic phase transitions. 

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