Exact enumeration results and figure data for "Unified origin of negative energetic elasticity in a lattice polymer chain: soft self-repulsion and bending stiffness"

This record contains the data files and plotting scripts used to generate (and/or directly provide the numerical content of) the figures in: Shirai, N. C. “Unified origin of negative energetic elasticity in a lattice polymer chain: soft self-repulsion and bending stiffness” Overview This study investigates the elastic response of a single lattice polymer chain with fixed end-to-end distance, incorporating both Domb–Joyce (DJ) soft-core self-repulsion and local bending-energy cost. The total energy is defined as: $$E(\omega) = \varepsilon m(\omega) + \varepsilon_b b(\omega)$$ where: $\varepsilon$ is the DJ self-repulsion strength $\varepsilon_b$ is the bending-energy cost $m(\omega)$ is the DJ overlap count $b(\omega)$ is the bend count Data Files Input Data File Description Format W_data.csv Enumeration data of random walks on a cubic lattice n,r,m,b,W Columns: n: Chain length (number of steps) r: End-to-end distance m: DJ overlap count (number of site overlaps) b: Bend count (number of direction changes) W: Number of configurations with given $(n, r, m, b)$, i.e., $W_{n,m,b}(r)$ Figure 1 data File Description Format Fig1_coordinate_data.csv Coordinates of a representative 20-step configuration i,x,y,z This file contains the coordinates of the configuration shown in Figure 1, demonstrating a 20-step random walk with endpoints fixed at the origin and $(10,0,0)$. Figure 2 data File Description Format Fig2_beta_k.csv Stiffness decomposition data beta_eps,beta_eps_b,beta_k,beta_kU,beta_kS Columns: beta_eps: Dimensionless DJ parameter $\beta\varepsilon$ beta_eps_b: Dimensionless bending parameter $\beta\varepsilon_b$ beta_k: Dimensionless total stiffness $\beta k$ beta_kU: Dimensionless energetic stiffness $\beta k_U$ beta_kS: Dimensionless entropic stiffness $\beta k_S$ Parameters: $(n, r) = (20, 10)$ Figure 3 data File Description Format Fig3_U_S.csv Internal energy and entropy vs end-to-end distance r,U,S Columns: r: End-to-end distance U: Internal energy $U/\varepsilon_b$ (in units of bending energy) S: Entropy $S/k_B$ (dimensionless) Parameters: $n=20$, $\varepsilon=0$, $\beta\varepsilon_b=1$ (bending-only limit) Figure 4 data File Description Format Fig4_U.csv Internal energy for various chain lengths and bending strengths n,r,beta_eps_b,U Columns: n: Chain length r: End-to-end distance beta_eps_b: Dimensionless bending parameter $\beta\varepsilon_b$ U: Internal energy $U/\varepsilon$ (in units of self-repulsion energy) Parameters: $\beta\varepsilon=1$, $\beta\varepsilon_b \in \lbrace 0, 2^{-6}, 2^{-4}, 2^{-2}\rbrace$, $n \in \lbrace 10, 11, \ldots, 20\rbrace$ Plotting scripts (Gnuplot, Figure 4) These scripts generate the Figure 4 plots from Fig4_U.csv. Script Description Output plot_Fig4_U_vs_n.plt Internal energy $U/\varepsilon$ vs $n$ Fig4_U_vs_n.pdf plot_Fig4_U_vs_slack.plt Internal energy $U/\varepsilon$ vs $(n-r)^{7/4}/n$ Fig4_U_vs_slack.pdf Shared configuration: config_plot_Fig4.plt (common settings and analytic fitting functions) Usage (Gnuplot) From the directory containing these files: gnuplot plot_Fig4_U_vs_n.plt gnuplot plot_Fig4_U_vs_slack.plt Dependencies Gnuplot Gnuplot 5.x or later (for .plt scripts) Tested environment Gnuplot 6.0 patchlevel 3 Citation If you use this data, please cite: Shirai, N. C. “Unified origin of negative energetic elasticity in a lattice polymer chain: soft self-repulsion and bending stiffness”