arXiv subjects

Eleftherios Mainas

Publications and source records attributed to Eleftherios Mainas.

2 recordsLinked to original sources

arXiv2025

The extraordinary importance of self-avoiding behavior in two-dimensional polymers: Insights from large-deviation theory

Some recent work pointed out the usefulness of taking a large-deviation perspective when trying to extract anything resembling a macroscopic order parameter from a computer simulation. In this paper we note that the end-to-end distance of polymers is such an order parameter. The presence of long-ranged excluded volume interactions leads to significant qualitative differences between the conformations of two- and three-dimensional polymers, some of which are difficult to quantify in computer simulations of realistic (off-lattice) polymer models. But we show here that phenomena such as the greatly enlarged non-Hooke's-law elasticity present in 2D are straightforward to extract from simulation using a large-deviation framework - even though simulating that nonlinearity is tantamount to simulating a 4th order susceptibility. The large-deviation perspective includes both a set of thermodynamic-like tools suitable for studying finite-size systems and a realization that an accurate description of the system's average behavior needs to be consistent with how improbably large fluctuations would behave in that system. The latter is key because strong correlations are absent in this asymptotic large fluctuation regime, so the regime's far-reaching effects can be analytically incorporated into the analysis of simulation data. That, in turn, allows us to direct the efforts of simulations away from difficult-to-sample rare-event domains. We illustrate this point with two- and three-dimensional Monte Carlo simulations (and exact results) on two models of a single isolated polymer chain: a chain of linked hard spheres, which has long-ranged excluded volume effects, and a discretized worm-like chain, which does not.

cond-mat.soft↗

arXiv2024

Exceptionally Large Fluctuations in Orientational Order: The Lessons of Large-Deviation Theory for Liquid Crystalline Systems

How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on isotropic-phase samples display increasingly large orientational fluctuations ("pseudo-nematic domains") as the samples approach their nematic phase. The growing length scale of those locally ordered domains is readily seen in simulation as an ever-slower convergence of the distribution of orientational order parameters with $N$. But the rare-event character and exceptionally slow time scales of the largest fluctuations make them difficult to sample accurately. We show in this paper how taking a large-deviation-theory perspective enables us to leverage simulation-derived information more effectively. A key insight of the theory is that finding quantities such as orientational order parameters (extensive variables), is completely equivalent to deducing the conjugate (intensive) thermodynamic field required to equilibrate that amount of order - and that knowing the relationship between the two (the "equation of state") can easily be turned into knowing the relative free energy of that degree of order. A variety of well-known thermodynamic integration strategies are already founded on this idea, but instead of applying an artificially imposed external field, we use a priori statistical mechanical insights into the small and large-field limits to construct a simulation-guided, interpolated, equation of state. The free energies that result mostly need information from the most probable configurations, making the simulation process far more efficient than waiting for (or artificially generating) large fluctuations.

cond-mat.soft↗