Generalized Statistical Mechanics and Scaling Behavior for Non-equilibrium Polymer Chains: I. Monomers Connected by Rigid Bonds

Physical mechanism for biopolymers to aggregate and maintain in non-equilibrium states

“…Otherwise, in the case of k n.n. = ∞, a scheme 51 is applied to generate constraint force keeping r ij numerically strictly to the value b ij . The ruggedness along the backbone of each chain is specified by the angle potentials in the third and the fourth summations of U .…”

“…Over the processes along the red dashed line on the right side of Fig. 1(e), the probability density function P GMB ( v ) for monomer speed v at each instant is well fitted by the generalized Maxwell-Boltzmann (GMB) speed distributionwhere the factor j G ( v ) = 4 πv 2 has been used in previous studies 51, 52 and A q is the normalization factor and all monomers are assumed to have equal masses, m  = 1. Note that, the choice of factor 4 πv 2 is compatible with the isotropic Maxwell’s distribution of speed (subscript ‘IMB’ for istropic Maxwell-Botzmann), which isas the special case of q  = 1.…”

Molecular Dynamics Approach to Relaxation and Aggregation of Polymer Chains

“…For example, it has been found that critical behaviors of Ising-type spin models 2) and lattice hard-core particle models 3) can be understood from percolation transitions of properly defined clusters of the systems as in the case of random percolation models, 4) that many percolation models 5) or the Ising model 6) on different lattices has universal finitesize scaling functions, 7) and that transitions to synchronous chaos of the coupled-map lattice model 8) with both local and global couplings have nice universal and scaling behaviors. 9) We have used molecular dynamics (MD) simulations to study relaxation processes in various systems of polymer chains and Lennard-Jones (L-J) molecules; two neighboring monomers along a polymer chain are connected by a rigid bond 10) or a spring of strength k spring . 11) We find that the velocity distributions of monomers in a wide range of simulation time can be well described by Tsallis q-statistics 14), 15) and a single scaling function, where q ≥ 1 and q-statistics becomes the Maxwell-Boltzmann distribution when q → 1.…”

Backbone Connectivity and Collective Aggregation Phenomena in Polymer Systems

“…Since the distributions of the monomer velocities are known to deviate systematically from the standard Maxwell-Boltzmann with the increased strength of nearest neighbor bonding [16,17] and are described by the Tsallis q-statistics [18], if the system reaches a "quasi-steady state", it is inappropriate to use the existing thermostating methods that would force the simulated system to converge to a state described by standard Maxwell-Boltzmann statistics. A naive choice without imposing presumed statistics is simply controlling only the mean value of the kinetic distributions.…”