{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "0", "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "import logging\n", "import warnings\n", "\n", "import numpy as np\n", "\n", "np.set_printoptions(precision=4)\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "\n", "logger = logging.getLogger()\n", "logger.setLevel(logging.ERROR)" ] }, { "cell_type": "markdown", "id": "1", "metadata": {}, "source": [ "# Model system: 1D ideal gas in a linear external potential" ] }, { "cell_type": "markdown", "id": "2", "metadata": {}, "source": [ "Below we gain intuition for the analytical model included in the thermoextrap package. Specifically, we have a system with $N$ ideal gas (IG) particles with a single dimension of length $L$. The potential energy for each particle is only a function of the particle location, $U(x) = ax$ where $x$ is the position of a particle along the single dimension. In what follows, $\\beta=\\frac{1}{k_{B}T}$ is the inverse temperature and we set the energy associated with particular position due to the external potential, $a$, equal to 1. This does not lose any generality as only values of $\\beta$ or $L$ relative to $a$ matter.\n", "\n", "Though this system is simple and completely analytical, it can be used to test nearly all of the functionalities of the {mod}`thermoextrap` package. As a result, it is featured in the unit testing to ensure that the code is not only reproducible, but also produces physically correct results coinciding with theory. This code is located in the module {mod}`thermoextrap.idealgas`." ] }, { "cell_type": "code", "execution_count": 2, "id": "3", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import cmomy\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from thermoextrap import idealgas\n", "\n", "rng = cmomy.random.default_rng(seed=0)" ] }, { "cell_type": "code", "execution_count": 3, "id": "4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beta = 1.0\n", "npart = 1000\n", "nconfig = 10000\n", "\n", "fig, axes = plt.subplots(3, 2)\n", "\n", "\n", "def get_utest(npart, beta, vol, ndev=5, n=100):\n", " uave = idealgas.x_ave(beta, vol) * npart\n", " ustd = np.sqrt(idealgas.x_var(beta, vol) * npart)\n", " return np.linspace(-1.0, 1.0, n) * ndev * ustd + uave\n", "\n", "\n", "# Note for ideal gas model, vol = length\n", "vols = [1.0, 10.0]\n", "\n", "for vol, ax in zip(vols, axes.T):\n", " xvals = np.arange(0.0, vol, 0.0001)\n", "\n", " # There are functions to sample both position and potential energy values\n", " uvals = idealgas.u_sample((nconfig, npart), beta, vol)\n", " uhist, ubins = np.histogram(uvals, bins=\"auto\", density=True)\n", " ubincents = 0.5 * (ubins[:-1] + ubins[1:])\n", "\n", " # We can also just directly calculate the average or variance of the particle positions\n", " utest = get_utest(npart, beta, vol)\n", "\n", " # Or you can get the probability distribution of x or U\n", " ax[0].set_title(f\"L={vol}\")\n", " ax[0].plot(xvals, idealgas.x_prob(xvals, beta, vol))\n", " ax[1].plot(xvals, idealgas.x_cdf(xvals, beta, vol))\n", " ax[2].plot(ubincents, uhist, \"o\")\n", " ax[2].plot(utest, idealgas.u_prob(utest, npart, beta, vol))\n", "\n", "for a in axes[1, :]:\n", " a.set_xlabel(\"x\")\n", "for a in axes[2, :]:\n", " a.set_xlabel(f\"U for N={npart}\")\n", "for a, label in zip(axes[:, 0], [\"P(x)\", \"cdf(x)\", \"P(U)\"]):\n", " a.set_ylabel(label)\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "5", "metadata": {}, "source": [ "The probability of a particle residing at a particular location is $\\frac{e^{-\\beta a x}}{\\int_0^L e^{-\\beta a x} dx}$, shown in the top panel. The cumulative distribution function, which is used to randomly sample from the distribution $P(x)$, is shown in the middle. From $N$ random draws of $x$ distributed according to $P(x)$, you have a single configuration with $N$ particles. The potential energy for a single configuration is $a \\sum_i x_i$ and so by randomly sampling many configurations, we construct the potential energy distribution in the bottom panel. For a single particle, the potential energy distribution is identical to $P(x)$ since a single $x$ maps to exactly one potential energy. For many particles, however, the potential energy is a random variable composed of a sum of independent random variables and so the distribution is Gaussian, as confirmed by the bottom panel." ] }, { "cell_type": "code", "execution_count": 4, "id": "6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now look at behavior as a function of inverse temperature (at the same system sizes as above)\n", "\n", "betas = np.arange(0.1, 10.0, 0.5)\n", "colors = plt.cm.coolwarm_r(np.arange(0.0, 1.0, float(1.0 / len(betas))))\n", "\n", "fig, axes = plt.subplots(3, 2)\n", "\n", "for vol, ax in zip(vols, axes.T):\n", " xvals = np.arange(0.0, vol, 0.0001)\n", " ax[0].set_title(f\"L={vol}\")\n", " ax[0].plot(betas, idealgas.x_ave(betas, vol))\n", "\n", " for beta, color in zip(betas, colors):\n", " ax[1].plot(xvals, idealgas.x_prob(xvals, beta, vol), color=color)\n", " utest = get_utest(npart, beta, vol)\n", " ax[2].plot(utest, idealgas.u_prob(utest, npart, beta, vol), color=color)\n", "\n", " ax[0].set_xlabel(r\"$\\beta$\")\n", " ax[0].set_ylabel(r\"$\\langle x \\rangle$\")\n", " ax[1].set_xlabel(\"x\")\n", " ax[1].set_ylabel(\"P(x)\")\n", " ax[2].set_xlabel(f\"U for N={npart}\")\n", " ax[2].set_ylabel(\"P(U)\")\n", "\n", "\n", "fig.tight_layout()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7", "metadata": {}, "source": [ "A simple structural property of interest is the average $x$ value, which is plotted in the top panel as a function of $\\beta$. It's only non-linear over a very large temperature range, but it's a toy system so the physical temperature really isn't relevant anyway. Changes in $P(x)$ and $P(U)$ with temperature are shown as well with coloring by temperature, NOT inverse temperature (blue is the lowest $T$, highest $\\beta$). Clearly the configurational distributions will not overlap in their important regions and neither will the potential energy distributions, meaning perturbation won't work at some point. This is especially true as $L$ is increased.\n", "\n", "Below, we show $\\langle x \\rangle$ as a function of $L$ at various temperatures. Non-linearities arise at all temperatures to varying degrees." ] }, { "cell_type": "code", "execution_count": 5, "id": "8", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Behavior of average x as a function of L\n", "fig, ax = plt.subplots()\n", "vols = np.arange(0.5, 10.0, 0.5)\n", "\n", "for beta, color in zip(betas, colors):\n", " ax.plot(\n", " vols,\n", " idealgas.x_ave(beta, vols),\n", " color=color,\n", " label=rf\"$\\beta$ = {beta}\",\n", " )\n", "\n", "ax.set_xlabel(r\"$L$\")\n", "ax.set_ylabel(r\"$\\langle x \\rangle$\")\n", "\n", "fig.tight_layout()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9", "metadata": {}, "source": [ "For testing for physical accuracy, note that the {mod}`thermoextrap.idealgas` module also comes with analytical computations of the derivatives with respect to $\\beta$ of $\\langle x \\rangle$, $\\langle \\beta x \\rangle$, $-\\ln \\langle x \\rangle$, and $-\\ln \\langle \\beta x \\rangle$. This allows for \"exact\" extrapolations at a given order, or at least what the extrapolation at that order should be in the limit of infinite sampling. There is also a function to compute analytical derivatives, and hence extrapolations, with respect to $L$. As we will explore in other notebooks, these scenarios cover most cases of interest in extrapolating structural and thermodynamic properties. For more information, see [here](https://doi.org/10.1063/5.0014282)." ] }, { "cell_type": "code", "execution_count": null, "id": "10", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "hide_input": false, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.8" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 5 }