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  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Ensembles and the thermodynamic limit\n",
    "\n",
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/sandialabs/Polymers/main?labpath=docs%2Fsource%2F%2Fphysics%2Fsingle_chain%2Ffjc%2Fthermodynamics%2Fexample_thermodynamic_limit.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f57cf5ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "from polymers import physics\n",
    "FJC = physics.single_chain.fjc.thermodynamics.FJC"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47ce8f2b",
   "metadata": {},
   "source": [
    "## Isometric versus isotensional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d41d285",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "N_b_list = [6, 12, 24]\n",
    "gamma = np.linspace(1e-3, 99e-2, 100)\n",
    "for N_b in N_b_list:\n",
    "    fjc = FJC(N_b, 1, 1)\n",
    "    eta_isometric = fjc.isometric.nondimensional_force(gamma)\n",
    "    plt.plot(gamma, eta_isometric, label=r'$N_b=$' + str(N_b))\n",
    "gamma_isotensional = fjc.isotensional.nondimensional_end_to_end_length_per_link(eta_isometric)\n",
    "plt.plot(gamma_isotensional, eta_isometric, 'k--', label='isotensional')\n",
    "plt.legend()\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([0, 12])\n",
    "plt.xlabel(r'$\\gamma$')\n",
    "plt.ylabel(r'$\\eta$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a85500fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "for N_b in N_b_list:\n",
    "    fjc = FJC(N_b, 1, 1)\n",
    "    Delta_vartheta = fjc.isometric.nondimensional_relative_helmholtz_free_energy_per_link(gamma)\n",
    "    plt.plot(gamma, Delta_vartheta, label=r'$N_b=$' + str(N_b))\n",
    "Delta_vartheta_legendre = fjc.isometric.legendre.nondimensional_relative_helmholtz_free_energy_per_link(gamma)\n",
    "plt.plot(gamma, Delta_vartheta_legendre, 'k--', label='legendre')\n",
    "plt.legend()\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([0, 3])\n",
    "plt.xlabel(r'$\\gamma$')\n",
    "plt.ylabel(r'$\\Delta\\vartheta$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "818fe14b",
   "metadata": {},
   "outputs": [],
   "source": [
    "for N_b in N_b_list:\n",
    "    fjc = FJC(N_b, 1, 1)\n",
    "    P_eq = fjc.isometric.nondimensional_equilibrium_distribution(gamma)\n",
    "    plt.plot(gamma, P_eq, label=r'$N_b=$' + str(N_b))\n",
    "P_eq_legendre = fjc.isometric.legendre.nondimensional_equilibrium_distribution(gamma)\n",
    "plt.plot(gamma, P_eq_legendre, 'k--', label='legendre')\n",
    "plt.legend()\n",
    "plt.xlim([0, 1])\n",
    "plt.xlabel(r'$\\gamma$')\n",
    "plt.ylabel(r'$\\mathscr{P}_\\mathrm{eq}$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6bc47eeb",
   "metadata": {},
   "outputs": [],
   "source": [
    "for N_b in N_b_list:\n",
    "    fjc = FJC(N_b, 1, 1)\n",
    "    g_eq = fjc.isometric.nondimensional_equilibrium_radial_distribution(gamma)\n",
    "    plt.plot(gamma, g_eq, label=r'$N_b=$' + str(N_b))\n",
    "g_eq_legendre = fjc.isometric.legendre.nondimensional_equilibrium_radial_distribution(gamma)\n",
    "plt.plot(gamma, g_eq_legendre, 'k--', label='legendre')\n",
    "plt.legend()\n",
    "plt.xlim([0, 1])\n",
    "plt.xlabel(r'$\\gamma$')\n",
    "plt.ylabel(r'$\\mathscr{g}_\\mathrm{eq}$')\n",
    "plt.show()"
   ]
  }
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