Schroeder_6p1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "194250d0",
   "metadata": {},
   "source": [
    "# Tables and plots for Schroeder 6.1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f437b74",
   "metadata": {},
   "source": [
    "We have two Einstein solids, $A$ and $B$, which have $N_A$ and $N_B$ oscillators, respectively. The individual multiplicities of each solid are:\n",
    "$$\n",
    "        \\Omega_A(N_A,q_A) = {q_A+N_A-1\\choose q_A} = \\frac{(q_A+N_A-1)!}{q_A!(N_A-1)!}\n",
    "$$\n",
    "\n",
    "$$\n",
    "        \\Omega_B(N_B,q_B) = {q_B+N_B-1\\choose B_A} = \\frac{(q_B+N_B-1)!}{q_B!(N_B-1)!}\n",
    "$$\n",
    "\n",
    "while the total multiplicity with $q_{\\rm total} = q_A + q_B$ is\n",
    "  $ \\Omega_{\\rm total} = \\Omega_A \\times \\Omega_B$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e051a49b",
   "metadata": {},
   "source": [
    "## Imports and function definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4030f05a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from scipy.special import comb\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9909e114",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ein_mult(N, q):\n",
    "    \"\"\"\n",
    "    Calculate the Einstein solid multiplicity and return it as\n",
    "     an integer.\n",
    "    \"\"\"\n",
    "    return int(comb(q + N -1, q))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b6cdab7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ein_entropy_over_k(N, q):\n",
    "    \"\"\"\n",
    "    Calculate the Einstein solid entropy divided by k (so just the\n",
    "      ln of the multiplicity).\n",
    "    \"\"\"\n",
    "    return np.log(np.float64(ein_mult(N,q)))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "642ae466",
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_int(my_int, large=10**6):\n",
    "    \"\"\"\n",
    "    If my_int is larger than large, return an exponential form.\n",
    "      The right justification for ints should be log10(large) + 1.\n",
    "    \"\"\"\n",
    "    if my_int > large:\n",
    "        return \"{: .1e}\".format(my_int)\n",
    "    else:\n",
    "        return \"{:>8}\".format(my_int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "eaa7e6e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def round_to_n(num, sigfigs):\n",
    "    \"\"\"\n",
    "    Round off num to the specifie number of sigfigs (significant figures)\n",
    "    \"\"\"\n",
    "    if num == 0:\n",
    "        return num\n",
    "    else:\n",
    "        return round(num, -int(math.floor(math.log10(abs(num)))) + (sigfigs - 1))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "92cd5185",
   "metadata": {},
   "outputs": [],
   "source": [
    "def central_diff(array, index, delta=1):\n",
    "    \"\"\"\n",
    "    Calculate the derivative of array at index by central difference\n",
    "    \"\"\"\n",
    "    return (array[index + 1] - array[index - 1]) / (2 * delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "313fc79d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_diff(array, index, delta=1):\n",
    "    \"\"\"\n",
    "    Calculate the derivative of array at index by forward difference\n",
    "    \"\"\"\n",
    "    return (array[index + 1] - array[index]) / delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e26e78da",
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward_diff(array, index, delta=1):\n",
    "    \"\"\"\n",
    "    Calculate the derivative of array at index by backward difference\n",
    "    \"\"\"\n",
    "    return (array[index] - array[index - 1]) / delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "55283398",
   "metadata": {},
   "outputs": [],
   "source": [
    "def macrostate_table(N_A, N_B, q_tot, table=True, q_max=20):\n",
    "    \"\"\"\n",
    "    Step through q_A and q_B = q_tot - q_A and use ein_mult \n",
    "      to find Omega_A and Omega_B.\n",
    "    Total multiplicity from: Omega_tot = Omega_A * Omega_B\n",
    "   \n",
    "    Construct a table like in Schroeder with macrostates \n",
    "      and multiplicities for a system of two Einstein solids\n",
    "      and return an array of Omega_tot values.\n",
    "      \n",
    "    If table=False, don't print the table but return the array\n",
    "     of Omega_tot values.\n",
    "    \"\"\"\n",
    "    if table:\n",
    "        print(' q_A  Omega_A  S_A/k  T_A ',\n",
    "              ' q_B  Omega_B   S_B/k T_B ',\n",
    "              'Omega_tot S_tot/k')\n",
    "    tot_microstates = 0\n",
    "    # Collect values in arrays\n",
    "    Omega_A_array = np.zeros(q_tot+1)  \n",
    "    Omega_B_array = np.zeros(q_tot+1)  \n",
    "    Omega_tot_array = np.zeros(q_tot+1)\n",
    "    S_A_array = np.zeros(q_tot+1)  \n",
    "    S_B_array = np.zeros(q_tot+1)  \n",
    "    T_B_array = np.zeros(q_tot+1)\n",
    "    S_tot_array = np.zeros(q_tot+1)\n",
    "    \n",
    "    for q_A in range(q_max+5):\n",
    "        Omega_A_array[q_A] = ein_mult(N_A, q_A) \n",
    "        S_A_array[q_A] = ein_entropy_over_k(N_A, q_A) \n",
    "        \n",
    "        q_B = q_tot - q_A\n",
    "        Omega_B_array[q_A] = ein_mult(N_B, q_B) \n",
    "        S_B_array[q_A] = ein_entropy_over_k(N_B, q_B) \n",
    "\n",
    "        Omega_tot_array[q_A] = Omega_A_array[q_A] * Omega_B_array[q_A]\n",
    "        tot_microstates += Omega_tot_array[q_A]\n",
    "        S_tot_array[q_A] = np.log(np.float64(Omega_tot_array[q_A]))\n",
    "        \n",
    "    if table:\n",
    "        eps = 0.1  # in eV --> maybe 0.01 eV would make more sense?\n",
    "        kBoltz = 8.62e-5  # in eV/K\n",
    "        eps_over_k = eps / kBoltz  # convert q to K\n",
    "        for q_A in range(q_max+5):\n",
    "            q_B = q_tot - q_A\n",
    "            T_A = 0\n",
    "            T_B = 0\n",
    "            # Calculate derivatives by central or forward/backward differences\n",
    "            if q_A > 0 and q_A < q_tot:\n",
    "#                T_A = fac / central_diff(S_A_array, q_A) \n",
    "                T_B = -eps_over_k / central_diff(S_B_array, q_A) \n",
    "            elif q_A == 0:\n",
    "#                T_A = fac / forward_diff(S_A_array, q_A) \n",
    "                T_B = -eps_over_k / forward_diff(S_B_array, q_A)               \n",
    "            elif q_A == q_tot:\n",
    "#                T_A = fac / backward_diff(S_A_array, q_A) \n",
    "                T_B = -eps_over_k / backward_diff(S_B_array, q_A) \n",
    "            T_B_array[q_A] = T_B\n",
    "            T_A = round_to_n(T_A, 2)\n",
    "            T_B = round_to_n(T_B, 2)\n",
    "            print (f'{q_A:> 4} {convert_int(Omega_A_array[q_A])}  {S_A_array[q_A]:5.1f} {T_A:4.0f} ',\n",
    "                   f'{q_B:> 4} {convert_int(Omega_B_array[q_A])}  {S_B_array[q_A]:5.1f} {T_B:4.0f}',\n",
    "                   f'{convert_int(Omega_tot_array[q_A])}  {S_tot_array[q_A]:5.1f}')\n",
    "        print(f'Total microstates = {convert_int(tot_microstates)}')\n",
    "\n",
    "        return eps_over_k, S_A_array, S_B_array, T_B_array, S_tot_array"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff6a277a",
   "metadata": {},
   "source": [
    "## Schroeder Table and Figures for Problem 6.1\n",
    "\n",
    "The system has one oscillator ($N_A = 1$) while the reservoir has many ($N_B \\gg N_A$). There are $q_{\\text{tot}}$ total units of energy to divide between them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04dd6ca2",
   "metadata": {},
   "source": [
    "### Table of multiplicities, entropies, and reservoir temperature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "92654c1b",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " q_A  Omega_A  S_A/k  T_A   q_B  Omega_B   S_B/k T_B  Omega_tot S_tot/k\n",
      "   0      1.0    0.0    0   500  1.9e+115  265.4 6400  1.9e+115  265.4\n",
      "   1      1.0    0.0    0   499  1.5e+115  265.2 6400  1.5e+115  265.2\n",
      "   2      1.0    0.0    0   498  1.3e+115  265.1 6400  1.3e+115  265.1\n",
      "   3      1.0    0.0    0   497  1.1e+115  264.9 6400  1.1e+115  264.9\n",
      "   4      1.0    0.0    0   496  9.0e+114  264.7 6400  9.0e+114  264.7\n",
      "   5      1.0    0.0    0   495  7.5e+114  264.5 6400  7.5e+114  264.5\n",
      "   6      1.0    0.0    0   494  6.2e+114  264.3 6400  6.2e+114  264.3\n",
      "   7      1.0    0.0    0   493  5.2e+114  264.1 6300  5.2e+114  264.1\n",
      "   8      1.0    0.0    0   492  4.3e+114  264.0 6300  4.3e+114  264.0\n",
      "   9      1.0    0.0    0   491  3.6e+114  263.8 6300  3.6e+114  263.8\n",
      "  10      1.0    0.0    0   490  3.0e+114  263.6 6300  3.0e+114  263.6\n",
      "  11      1.0    0.0    0   489  2.5e+114  263.4 6300  2.5e+114  263.4\n",
      "  12      1.0    0.0    0   488  2.1e+114  263.2 6300  2.1e+114  263.2\n",
      "  13      1.0    0.0    0   487  1.7e+114  263.0 6300  1.7e+114  263.0\n",
      "  14      1.0    0.0    0   486  1.4e+114  262.9 6300  1.4e+114  262.9\n",
      "  15      1.0    0.0    0   485  1.2e+114  262.7 6300  1.2e+114  262.7\n",
      "  16      1.0    0.0    0   484  9.9e+113  262.5 6200  9.9e+113  262.5\n",
      "  17      1.0    0.0    0   483  8.2e+113  262.3 6200  8.2e+113  262.3\n",
      "  18      1.0    0.0    0   482  6.8e+113  262.1 6200  6.8e+113  262.1\n",
      "  19      1.0    0.0    0   481  5.6e+113  261.9 6200  5.6e+113  261.9\n",
      "  20      1.0    0.0    0   480  4.7e+113  261.7 6200  4.7e+113  261.7\n",
      "  21      1.0    0.0    0   479  3.9e+113  261.5 6200  3.9e+113  261.5\n",
      "  22      1.0    0.0    0   478  3.2e+113  261.4 6200  3.2e+113  261.4\n",
      "  23      1.0    0.0    0   477  2.7e+113  261.2 6200  2.7e+113  261.2\n",
      "  24      1.0    0.0    0   476  2.2e+113  261.0    9  2.2e+113  261.0\n",
      "Total microstates =  1.1e+116\n"
     ]
    }
   ],
   "source": [
    "N_A = 1\n",
    "N_B = 100\n",
    "q_tot = 500\n",
    "q_max = 20  # number of q_A values to print and plot\n",
    "\n",
    "eps_over_k, S_A_array, S_B_array, T_B_array, S_tot_array = macrostate_table(N_A, N_B, q_tot, q_max=q_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2286880d",
   "metadata": {},
   "source": [
    "### First plot the total multiplicity as a function of $q_A$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "06c013f2",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax0 = plt.subplots(1, 1)\n",
    "q_array = np.arange(len(S_tot_array))\n",
    "ax0.scatter(q_array, np.exp(S_tot_array), label=r'$\\Omega_{\\rm tot}$', color='red')\n",
    "\n",
    "ax0.set_xlabel(r'$q_A$ (energy in units of $\\varepsilon$)')\n",
    "ax0.set_ylabel(r'Total multiplicity')\n",
    "ax0.set_xlim(q_array[0], q_array[int(q_max)])\n",
    "#ax0.set_ylim(np.floor(eS_tot_array[int(q_max)]), np.ceil(S_tot_array[0]))\n",
    "ax0.set_xticks(np.arange(0, q_array[int(q_max)]+1, 5));\n",
    "#fig.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4142be2e",
   "metadata": {},
   "source": [
    "### Now plot the total entropy as a function of $q_A$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "54d3aa6c",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax0 = plt.subplots(1, 1)\n",
    "q_array = np.arange(len(S_tot_array))\n",
    "ax0.scatter(q_array, S_tot_array, label=r'$S_{\\rm tot}$', color='red')\n",
    "\n",
    "ax0.set_xlabel(r'$q_A$ (energy in units of $\\varepsilon$)')\n",
    "ax0.set_ylabel(r'Total entropy (units of $k$)')\n",
    "ax0.set_xlim(q_array[0], q_array[int(q_max)])\n",
    "ax0.set_ylim(np.floor(S_tot_array[int(q_max)]), np.ceil(S_tot_array[0]))\n",
    "ax0.set_xticks(np.arange(0, q_array[int(q_max)]+1, 5));\n",
    "#fig.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cbf4aba",
   "metadata": {},
   "source": [
    "### Repeat the last plot using a Boltzmann factor exponent as slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a6047fb4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax0 = plt.subplots(1, 1)\n",
    "q_array = np.arange(len(S_tot_array))\n",
    "ax0.scatter(q_array, S_tot_array, label=r'$S_{\\rm tot}$', color='red')\n",
    "ax0.plot(q_array[0:q_max+1], S_tot_array[0] - eps_over_k/T_B_array[0:q_max+1]*q_array[0:q_max+1], color='green')\n",
    "\n",
    "ax0.set_xlabel(r'$q_A$ (energy in units of $\\varepsilon$)')\n",
    "ax0.set_ylabel(r'Total entropy (units of $k$)')\n",
    "ax0.set_xlim(q_array[0], q_array[int(q_max)])\n",
    "ax0.set_ylim(np.floor(S_tot_array[int(q_max)]), np.ceil(S_tot_array[0]))\n",
    "ax0.set_xticks(np.arange(0, q_array[int(q_max)]+1, 5));\n",
    "#fig.legend();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}