Static and dynamic properties of discrete systems with compressed state space. A polymer chain as an example

The method of the reduction of the size of the state space based on its symmetry is presented. An important property of the method is that in its static version, it preserves probabilities of states of the system. In the reduced state space, the probability of a new state (termed below as class) is equal to the probability of each of the states belonging to a given class multiplied by the number of states which form this class. We also present an appropriate method which allows to calculate time dependent probabilities of states of a given system, if multiple absorbing states are present. This is done with a continuous version of the exact enumeration method for weighted networks. The approach provides a new method of the analysis of non-equilibrium processes. As an application, the state space of a polymer molecule is analysed. We model circular polymer on a regular 2D square lattice. The reduction of the size of the system is presented, as dependent on external conditions. Finally, we evaluate the time of relaxation to and from the absorbing states.