Partition function expanded ensembles

The goal of the method is to perform a random walk in space. Consider a system consisting of N particles interconnected to form a molecule, and having volume V and temperature T. The end-to-end distance of the molecule ( ) can be discretized into distinct states each state is characterized by its end-to-end distance, in some specified range of interest [, +j and represent a lower and an upper bound, respectively. The partition function 17 of this expanded ensemble is given by... 

Formally, an expanded canonical ensemble can be defined through the partition function ... 

A = Helmholtz free energy A(x y) = acceptance probability between states y and x H = Hamiltonian of a system h = molecular enthalpy K x, y) = transition probability between states y and x ks = Boltzmann constant M = number of states in an expanded ensemble m = mass of a particle N = total number of particles in the system A samp = number of trial orientation for segmental regrowth P = pressure of the system p = probability of a given state Q = canonical Partition function = Ro.senbluth weight =... 

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