Einstein_solid_counting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "194250d0",
   "metadata": {},
   "source": [
    "# Calculating and plotting Einstein solids\n",
    "\n",
    "We'll follow the notation in the Schroeder text in sections 2.2 and 2.3.\n",
    "\n",
    "The multiplicity for a single Einstein solid with $N$ oscillators and total energy $q$ (in units of $hf$) is:\n",
    "$$\n",
    "        \\Omega(N,q) = {q+N-1\\choose q} = \\frac{(q+N-1)!}{q!(N-1)!}\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4030f05a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\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": "markdown",
   "id": "8e6a43d8",
   "metadata": {},
   "source": [
    "## Schroeder section 2.2 Einstein model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "042cd686",
   "metadata": {},
   "source": [
    "### Problem 2.5\n",
    "For an Einstein solid with each of the following values of $N$ and $q$, list all of the possible microstates, count them, and verify the multiplicity formula.\n",
    "\n",
    "(a) $N=3$, $q=4$ <br>\n",
    "(b) $N=3$, $q=5$ <br>\n",
    "(c) $N=3$, $q=6$ <br>\n",
    "(d) $N=4$, $q=2$ <br>\n",
    "(e) $N=4$, $q=3$ <br>\n",
    "(f) $N=1$, $q=\\mbox{anything}$ <br>\n",
    "(g) $N=\\mbox{anything}$, $q=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "588eca42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ein_mult(10, 1)  # 2.5(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "62224238",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ein_mult(4, 3)  # 2.5(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "237a70a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ein_mult(1, 20)  # 2.5(f) --> try other q values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e3a7314",
   "metadata": {},
   "source": [
    "### Problem 2.6\n",
    "\n",
    "Calculate the multiplicity of an Einstein solid with 30 oscillators and 30 units of energy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0e7f3887",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "answer = 5.91e+16\n"
     ]
    }
   ],
   "source": [
    "print(f'answer = {ein_mult(30, 30):.2e}') # print 3 sig figs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27d1c44e",
   "metadata": {},
   "source": [
    "## Section 2.3 Interacting systems"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28a50b99",
   "metadata": {},
   "source": [
    "Now 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": "code",
   "execution_count": 7,
   "id": "642ae466",
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_int(my_int, large=10**7):\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": 8,
   "id": "55283398",
   "metadata": {},
   "outputs": [],
   "source": [
    "def macrostate_table(N_A, N_B, q_tot, table=True):\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     q_B      Omega_B   Omega_tot')\n",
    "    tot_microstates = 0\n",
    "    Omega_tot_array = np.zeros(q_tot+1)  # collect Omega_tot values\n",
    "    for q_A in range(q_tot+1):\n",
    "        Omega_A = ein_mult(N_A, q_A) \n",
    "        \n",
    "        q_B = q_tot - q_A\n",
    "        Omega_B = ein_mult(N_B, q_B) \n",
    "\n",
    "        Omega_tot = Omega_A * Omega_B\n",
    "        Omega_tot_array[q_A] = Omega_tot\n",
    "        tot_microstates += Omega_tot\n",
    "        \n",
    "        if table:\n",
    "            print (f' {q_A:> 4}   {convert_int(Omega_A)}     {q_B:> 4}',\n",
    "                   f'   {convert_int(Omega_B)}  ',\n",
    "                   f'{convert_int(Omega_tot)}')\n",
    "    print(f'Total microstates = {convert_int(tot_microstates)}')\n",
    "    return Omega_tot_array"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "847eef25",
   "metadata": {},
   "source": [
    "### Figure 2.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9dd5ddf8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  q_A     Omega_A     q_B      Omega_B   Omega_tot\n",
      "    0          1        6          28         28\n",
      "    1          3        5          21         63\n",
      "    2          6        4          15         90\n",
      "    3         10        3          10        100\n",
      "    4         15        2           6         90\n",
      "    5         21        1           3         63\n",
      "    6         28        0           1         28\n",
      "Total microstates =      462\n"
     ]
    }
   ],
   "source": [
    "Omega_tot_array = macrostate_table(3, 3, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5763be9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 28.,  63.,  90., 100.,  90.,  63.,  28.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omega_tot_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "08d0ddb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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(Omega_tot_array))\n",
    "ax0.bar(q_array, Omega_tot_array, edgecolor='blue', color='lightblue')\n",
    "ax0.set_xlabel(r'$q_A$')\n",
    "ax0.set_ylabel(r'total multiplicity $\\Omega_{\\rm total}$ given $q_A$')\n",
    "#ax0.set_xlim(q_array[0], q_array[-1])\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efdc916a",
   "metadata": {},
   "source": [
    "### Figure 2.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "962537a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  q_A     Omega_A     q_B      Omega_B   Omega_tot\n",
      "    0          1      100     2.8e+81    2.8e+81\n",
      "    1        300       99     9.3e+80    2.8e+83\n",
      "    2      45150       98     3.1e+80    1.4e+85\n",
      "    3    4545100       97     1.0e+80    4.6e+86\n",
      "    4    3.4e+08       96     3.3e+79    1.1e+88\n",
      "    5    2.1e+10       95     1.1e+79    2.3e+89\n",
      "    6    1.1e+12       94     3.5e+78    3.7e+90\n",
      "    7    4.7e+13       93     1.1e+78    5.2e+91\n",
      "    8    1.8e+15       92     3.6e+77    6.4e+92\n",
      "    9    6.1e+16       91     1.1e+77    6.9e+93\n",
      "   10    1.9e+18       90     3.6e+76    6.7e+94\n",
      "   11    5.3e+19       89     1.1e+76    5.9e+95\n",
      "   12    1.4e+21       88     3.4e+75    4.7e+96\n",
      "   13    3.3e+22       87     1.0e+75    3.5e+97\n",
      "   14    7.4e+23       86     3.2e+74    2.4e+98\n",
      "   15    1.5e+25       85     9.6e+73    1.5e+99\n",
      "   16    3.0e+26       84     2.9e+73    8.8e+99\n",
      "   17    5.7e+27       83     8.5e+72    4.8e+100\n",
      "   18    1.0e+29       82     2.5e+72    2.5e+101\n",
      "   19    1.7e+30       81     7.3e+71    1.2e+102\n",
      "   20    2.7e+31       80     2.1e+71    5.7e+102\n",
      "   21    4.1e+32       79     6.1e+70    2.5e+103\n",
      "   22    5.9e+33       78     1.7e+70    1.0e+104\n",
      "   23    8.3e+34       77     4.9e+69    4.0e+104\n",
      "   24    1.1e+36       76     1.4e+69    1.5e+105\n",
      "   25    1.4e+37       75     3.8e+68    5.4e+105\n",
      "   26    1.8e+38       74     1.0e+68    1.9e+106\n",
      "   27    2.2e+39       73     2.8e+67    6.1e+106\n",
      "   28    2.5e+40       72     7.5e+66    1.9e+107\n",
      "   29    2.9e+41       71     2.0e+66    5.7e+107\n",
      "   30    3.2e+42       70     5.2e+65    1.7e+108\n",
      "   31    3.4e+43       69     1.4e+65    4.6e+108\n",
      "   32    3.5e+44       68     3.5e+64    1.2e+109\n",
      "   33    3.5e+45       67     8.9e+63    3.1e+109\n",
      "   34    3.4e+46       66     2.2e+63    7.7e+109\n",
      "   35    3.3e+47       65     5.6e+62    1.8e+110\n",
      "   36    3.0e+48       64     1.4e+62    4.2e+110\n",
      "   37    2.8e+49       63     3.4e+61    9.3e+110\n",
      "   38    2.5e+50       62     8.1e+60    2.0e+111\n",
      "   39    2.1e+51       61     1.9e+60    4.1e+111\n",
      "   40    1.8e+52       60     4.5e+59    8.1e+111\n",
      "   41    1.5e+53       59     1.0e+59    1.6e+112\n",
      "   42    1.2e+54       58     2.4e+58    2.9e+112\n",
      "   43    9.7e+54       57     5.4e+57    5.2e+112\n",
      "   44    7.5e+55       56     1.2e+57    9.0e+112\n",
      "   45    5.8e+56       55     2.6e+56    1.5e+113\n",
      "   46    4.3e+57       54     5.7e+55    2.5e+113\n",
      "   47    3.2e+58       53     1.2e+55    3.9e+113\n",
      "   48    2.3e+59       52     2.6e+54    5.9e+113\n",
      "   49    1.6e+60       51     5.3e+53    8.6e+113\n",
      "   50    1.1e+61       50     1.1e+53    1.2e+114\n",
      "   51    7.8e+61       49     2.2e+52    1.7e+114\n",
      "   52    5.3e+62       48     4.3e+51    2.3e+114\n",
      "   53    3.5e+63       47     8.3e+50    2.9e+114\n",
      "   54    2.3e+64       46     1.6e+50    3.6e+114\n",
      "   55    1.5e+65       45     3.0e+49    4.4e+114\n",
      "   56    9.3e+65       44     5.5e+48    5.1e+114\n",
      "   57    5.8e+66       43     1.0e+48    5.8e+114\n",
      "   58    3.6e+67       42     1.8e+47    6.4e+114\n",
      "   59    2.2e+68       41     3.1e+46    6.7e+114\n",
      "   60    1.3e+69       40     5.3e+45    6.9e+114\n",
      "   61    7.7e+69       39     8.8e+44    6.8e+114\n",
      "   62    4.5e+70       38     1.4e+44    6.5e+114\n",
      "   63    2.6e+71       37     2.3e+43    6.0e+114\n",
      "   64    1.5e+72       36     3.6e+42    5.3e+114\n",
      "   65    8.2e+72       35     5.6e+41    4.5e+114\n",
      "   66    4.5e+73       34     8.3e+40    3.8e+114\n",
      "   67    2.5e+74       33     1.2e+40    3.0e+114\n",
      "   68    1.3e+75       32     1.7e+39    2.3e+114\n",
      "   69    7.1e+75       31     2.4e+38    1.7e+114\n",
      "   70    3.7e+76       30     3.2e+37    1.2e+114\n",
      "   71    2.0e+77       29     4.2e+36    8.2e+113\n",
      "   72    1.0e+78       28     5.4e+35    5.4e+113\n",
      "   73    5.1e+78       27     6.6e+34    3.4e+113\n",
      "   74    2.6e+79       26     7.9e+33    2.0e+113\n",
      "   75    1.3e+80       25     9.2e+32    1.2e+113\n",
      "   76    6.4e+80       24     1.0e+32    6.5e+112\n",
      "   77    3.1e+81       23     1.1e+31    3.4e+112\n",
      "   78    1.5e+82       22     1.1e+30    1.7e+112\n",
      "   79    7.2e+82       21     1.1e+29    8.1e+111\n",
      "   80    3.4e+83       20     1.1e+28    3.7e+111\n",
      "   81    1.6e+84       19     9.9e+26    1.6e+111\n",
      "   82    7.4e+84       18     8.6e+25    6.4e+110\n",
      "   83    3.4e+85       17     7.1e+24    2.4e+110\n",
      "   84    1.6e+86       16     5.6e+23    8.8e+109\n",
      "   85    7.0e+86       15     4.2e+22    2.9e+109\n",
      "   86    3.1e+87       14     2.9e+21    9.2e+108\n",
      "   87    1.4e+88       13     1.9e+20    2.7e+108\n",
      "   88    6.1e+88       12     1.2e+19    7.3e+107\n",
      "   89    2.7e+89       11     6.7e+17    1.8e+107\n",
      "   90    1.2e+90       10     3.5e+16    4.1e+106\n",
      "   91    5.0e+90        9     1.7e+15    8.4e+105\n",
      "   92    2.1e+91        8     7.3e+13    1.5e+105\n",
      "   93    8.9e+91        7     2.8e+12    2.5e+104\n",
      "   94    3.7e+92        6     9.6e+10    3.6e+103\n",
      "   95    1.5e+93        5     2.8e+09    4.3e+102\n",
      "   96    6.3e+93        4     6.9e+07    4.4e+101\n",
      "   97    2.6e+94        3     1353400    3.5e+100\n",
      "   98    1.0e+95        2       20100    2.1e+99\n",
      "   99    4.2e+95        1         200    8.4e+97\n",
      "  100    1.7e+96        0           1    1.7e+96\n",
      "Total microstates =  9.3e+115\n"
     ]
    }
   ],
   "source": [
    "Omega_tot_array = macrostate_table(300, 200, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6b7954f7",
   "metadata": {},
   "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(Omega_tot_array))\n",
    "ax0.plot(q_array, Omega_tot_array, color='blue')\n",
    "ax0.fill_between(q_array, Omega_tot_array, color='lightblue')\n",
    "ax0.set_xlabel(r'$q_A$')\n",
    "ax0.set_ylabel(r'total multiplicity $\\Omega_{\\rm total}$')\n",
    "ax0.set_xlim(q_array[0], q_array[-1])\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6b25ce4",
   "metadata": {},
   "source": [
    "### Test the upper limit of system size\n",
    "\n",
    "The largest float in Python is about $2.3\\times 10^{308}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3b744531",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  q_A     Omega_A     q_B      Omega_B   Omega_tot\n",
      "    0          1      300     1.3e+228    1.3e+228\n",
      "    1        500      299     4.8e+227    2.4e+230\n",
      "    2     125250      298     1.8e+227    2.3e+232\n",
      "    3    2.1e+07      297     6.8e+226    1.4e+234\n",
      "    4    2.6e+09      296     2.5e+226    6.7e+235\n",
      "    5    2.7e+11      295     9.4e+225    2.5e+237\n",
      "    6    2.2e+13      294     3.5e+225    7.8e+238\n",
      "    7    1.6e+15      293     1.3e+225    2.1e+240\n",
      "    8    1.0e+17      292     4.8e+224    4.9e+241\n",
      "    9    5.8e+18      291     1.8e+224    1.0e+243\n",
      "   10    2.9e+20      290     6.5e+223    1.9e+244\n",
      "   11    1.4e+22      289     2.4e+223    3.3e+245\n",
      "   12    5.8e+23      288     8.8e+222    5.1e+246\n",
      "   13    2.3e+25      287     3.2e+222    7.4e+247\n",
      "   14    8.4e+26      286     1.2e+222    9.9e+248\n",
      "   15    2.9e+28      285     4.3e+221    1.2e+250\n",
      "   16    9.2e+29      284     1.6e+221    1.4e+251\n",
      "   17    2.8e+31      283     5.7e+220    1.6e+252\n",
      "   18    8.1e+32      282     2.0e+220    1.6e+253\n",
      "   19    2.2e+34      281     7.4e+219    1.6e+254\n",
      "   20    5.7e+35      280     2.7e+219    1.5e+255\n",
      "   21    1.4e+37      279     9.6e+218    1.4e+256\n",
      "   22    3.3e+38      278     3.4e+218    1.1e+257\n",
      "   23    7.6e+39      277     1.2e+218    9.3e+257\n",
      "   24    1.7e+41      276     4.4e+217    7.2e+258\n",
      "   25    3.5e+42      275     1.6e+217    5.4e+259\n",
      "   26    7.0e+43      274     5.5e+216    3.9e+260\n",
      "   27    1.4e+45      273     2.0e+216    2.7e+261\n",
      "   28    2.6e+46      272     6.9e+215    1.8e+262\n",
      "   29    4.7e+47      271     2.5e+215    1.1e+263\n",
      "   30    8.2e+48      270     8.6e+214    7.1e+263\n",
      "   31    1.4e+50      269     3.0e+214    4.3e+264\n",
      "   32    2.3e+51      268     1.1e+214    2.5e+265\n",
      "   33    3.8e+52      267     3.7e+213    1.4e+266\n",
      "   34    5.9e+53      266     1.3e+213    7.6e+266\n",
      "   35    9.0e+54      265     4.5e+212    4.1e+267\n",
      "   36    1.3e+56      264     1.6e+212    2.1e+268\n",
      "   37    1.9e+57      263     5.4e+211    1.0e+269\n",
      "   38    2.7e+58      262     1.9e+211    5.1e+269\n",
      "   39    3.8e+59      261     6.4e+210    2.4e+270\n",
      "   40    5.1e+60      260     2.2e+210    1.1e+271\n",
      "   41    6.7e+61      259     7.5e+209    5.1e+271\n",
      "   42    8.7e+62      258     2.6e+209    2.2e+272\n",
      "   43    1.1e+64      257     8.8e+208    9.6e+272\n",
      "   44    1.3e+65      256     3.0e+208    4.0e+273\n",
      "   45    1.6e+66      255     1.0e+208    1.6e+274\n",
      "   46    1.9e+67      254     3.4e+207    6.6e+274\n",
      "   47    2.2e+68      253     1.2e+207    2.6e+275\n",
      "   48    2.6e+69      252     3.9e+206    9.9e+275\n",
      "   49    2.9e+70      251     1.3e+206    3.7e+276\n",
      "   50    3.1e+71      250     4.4e+205    1.4e+277\n",
      "   51    3.4e+72      249     1.5e+205    4.9e+277\n",
      "   52    3.6e+73      248     4.8e+204    1.7e+278\n",
      "   53    3.7e+74      247     1.6e+204    6.0e+278\n",
      "   54    3.8e+75      246     5.3e+203    2.0e+279\n",
      "   55    3.8e+76      245     1.8e+203    6.8e+279\n",
      "   56    3.8e+77      244     5.8e+202    2.2e+280\n",
      "   57    3.7e+78      243     1.9e+202    7.1e+280\n",
      "   58    3.6e+79      242     6.2e+201    2.2e+281\n",
      "   59    3.4e+80      241     2.0e+201    6.9e+281\n",
      "   60    3.1e+81      240     6.6e+200    2.1e+282\n",
      "   61    2.9e+82      239     2.2e+200    6.2e+282\n",
      "   62    2.6e+83      238     7.0e+199    1.8e+283\n",
      "   63    2.3e+84      237     2.3e+199    5.2e+283\n",
      "   64    2.1e+85      236     7.2e+198    1.5e+284\n",
      "   65    1.8e+86      235     2.3e+198    4.1e+284\n",
      "   66    1.5e+87      234     7.5e+197    1.1e+285\n",
      "   67    1.3e+88      233     2.4e+197    3.1e+285\n",
      "   68    1.1e+89      232     7.6e+196    8.1e+285\n",
      "   69    8.8e+89      231     2.4e+196    2.1e+286\n",
      "   70    7.2e+90      230     7.6e+195    5.5e+286\n",
      "   71    5.8e+91      229     2.4e+195    1.4e+287\n",
      "   72    4.6e+92      228     7.5e+194    3.4e+287\n",
      "   73    3.6e+93      227     2.4e+194    8.5e+287\n",
      "   74    2.8e+94      226     7.4e+193    2.1e+288\n",
      "   75    2.1e+95      225     2.3e+193    4.9e+288\n",
      "   76    1.6e+96      224     7.2e+192    1.2e+289\n",
      "   77    1.2e+97      223     2.2e+192    2.7e+289\n",
      "   78    8.9e+97      222     6.9e+191    6.1e+289\n",
      "   79    6.5e+98      221     2.1e+191    1.4e+290\n",
      "   80    4.7e+99      220     6.5e+190    3.1e+290\n",
      "   81    3.4e+100      219     2.0e+190    6.7e+290\n",
      "   82    2.4e+101      218     6.0e+189    1.4e+291\n",
      "   83    1.7e+102      217     1.8e+189    3.1e+291\n",
      "   84    1.2e+103      216     5.6e+188    6.5e+291\n",
      "   85    8.0e+103      215     1.7e+188    1.3e+292\n",
      "   86    5.4e+104      214     5.1e+187    2.8e+292\n",
      "   87    3.7e+105      213     1.5e+187    5.6e+292\n",
      "   88    2.4e+106      212     4.6e+186    1.1e+293\n",
      "   89    1.6e+107      211     1.4e+186    2.2e+293\n",
      "   90    1.1e+108      210     4.0e+185    4.3e+293\n",
      "   91    6.8e+108      209     1.2e+185    8.2e+293\n",
      "   92    4.4e+109      208     3.5e+184    1.6e+294\n",
      "   93    2.8e+110      207     1.0e+184    2.9e+294\n",
      "   94    1.8e+111      206     3.0e+183    5.4e+294\n",
      "   95    1.1e+112      205     8.9e+182    9.8e+294\n",
      "   96    6.8e+112      204     2.6e+182    1.8e+295\n",
      "   97    4.2e+113      203     7.5e+181    3.2e+295\n",
      "   98    2.6e+114      202     2.2e+181    5.6e+295\n",
      "   99    1.5e+115      201     6.3e+180    9.7e+295\n",
      "  100    9.3e+115      200     1.8e+180    1.7e+296\n",
      "  101    5.5e+116      199     5.1e+179    2.8e+296\n",
      "  102    3.2e+117      198     1.5e+179    4.8e+296\n",
      "  103    1.9e+118      197     4.2e+178    7.9e+296\n",
      "  104    1.1e+119      196     1.2e+178    1.3e+297\n",
      "  105    6.3e+119      195     3.3e+177    2.1e+297\n",
      "  106    3.6e+120      194     9.3e+176    3.4e+297\n",
      "  107    2.0e+121      193     2.6e+176    5.3e+297\n",
      "  108    1.1e+122      192     7.3e+175    8.4e+297\n",
      "  109    6.4e+122      191     2.0e+175    1.3e+298\n",
      "  110    3.5e+123      190     5.6e+174    2.0e+298\n",
      "  111    1.9e+124      189     1.5e+174    3.0e+298\n",
      "  112    1.1e+125      188     4.3e+173    4.5e+298\n",
      "  113    5.8e+125      187     1.2e+173    6.7e+298\n",
      "  114    3.1e+126      186     3.2e+172    9.8e+298\n",
      "  115    1.7e+127      185     8.6e+171    1.4e+299\n",
      "  116    8.8e+127      184     2.3e+171    2.0e+299\n",
      "  117    4.6e+128      183     6.3e+170    2.9e+299\n",
      "  118    2.4e+129      182     1.7e+170    4.1e+299\n",
      "  119    1.3e+130      181     4.5e+169    5.6e+299\n",
      "  120    6.5e+130      180     1.2e+169    7.7e+299\n",
      "  121    3.3e+131      179     3.2e+168    1.1e+300\n",
      "  122    1.7e+132      178     8.4e+167    1.4e+300\n",
      "  123    8.5e+132      177     2.2e+167    1.9e+300\n",
      "  124    4.3e+133      176     5.8e+166    2.5e+300\n",
      "  125    2.1e+134      175     1.5e+166    3.2e+300\n",
      "  126    1.1e+135      174     3.9e+165    4.1e+300\n",
      "  127    5.2e+135      173     1.0e+165    5.3e+300\n",
      "  128    2.6e+136      172     2.6e+164    6.7e+300\n",
      "  129    1.2e+137      171     6.7e+163    8.3e+300\n",
      "  130    6.0e+137      170     1.7e+163    1.0e+301\n",
      "  131    2.9e+138      169     4.3e+162    1.3e+301\n",
      "  132    1.4e+139      168     1.1e+162    1.5e+301\n",
      "  133    6.6e+139      167     2.8e+161    1.8e+301\n",
      "  134    3.1e+140      166     6.9e+160    2.1e+301\n",
      "  135    1.5e+141      165     1.7e+160    2.5e+301\n",
      "  136    6.8e+141      164     4.3e+159    2.9e+301\n",
      "  137    3.2e+142      163     1.1e+159    3.4e+301\n",
      "  138    1.5e+143      162     2.6e+158    3.8e+301\n",
      "  139    6.7e+143      161     6.4e+157    4.3e+301\n",
      "  140    3.1e+144      160     1.6e+157    4.8e+301\n",
      "  141    1.4e+145      159     3.8e+156    5.3e+301\n",
      "  142    6.3e+145      158     9.2e+155    5.7e+301\n",
      "  143    2.8e+146      157     2.2e+155    6.2e+301\n",
      "  144    1.3e+147      156     5.3e+154    6.6e+301\n",
      "  145    5.6e+147      155     1.3e+154    7.0e+301\n",
      "  146    2.5e+148      154     3.0e+153    7.3e+301\n",
      "  147    1.1e+149      153     7.0e+152    7.6e+301\n",
      "  148    4.7e+149      152     1.6e+152    7.8e+301\n",
      "  149    2.1e+150      151     3.8e+151    7.9e+301\n",
      "  150    8.9e+150      150     8.9e+150    8.0e+301\n",
      "  151    3.8e+151      149     2.1e+150    7.9e+301\n",
      "  152    1.6e+152      148     4.7e+149    7.8e+301\n",
      "  153    7.0e+152      147     1.1e+149    7.6e+301\n",
      "  154    3.0e+153      146     2.5e+148    7.3e+301\n",
      "  155    1.3e+154      145     5.6e+147    7.0e+301\n",
      "  156    5.3e+154      144     1.3e+147    6.6e+301\n",
      "  157    2.2e+155      143     2.8e+146    6.2e+301\n",
      "  158    9.2e+155      142     6.3e+145    5.7e+301\n",
      "  159    3.8e+156      141     1.4e+145    5.3e+301\n",
      "  160    1.6e+157      140     3.1e+144    4.8e+301\n",
      "  161    6.4e+157      139     6.7e+143    4.3e+301\n",
      "  162    2.6e+158      138     1.5e+143    3.8e+301\n",
      "  163    1.1e+159      137     3.2e+142    3.4e+301\n",
      "  164    4.3e+159      136     6.8e+141    2.9e+301\n",
      "  165    1.7e+160      135     1.5e+141    2.5e+301\n",
      "  166    6.9e+160      134     3.1e+140    2.1e+301\n",
      "  167    2.8e+161      133     6.6e+139    1.8e+301\n",
      "  168    1.1e+162      132     1.4e+139    1.5e+301\n",
      "  169    4.3e+162      131     2.9e+138    1.3e+301\n",
      "  170    1.7e+163      130     6.0e+137    1.0e+301\n",
      "  171    6.7e+163      129     1.2e+137    8.3e+300\n",
      "  172    2.6e+164      128     2.6e+136    6.7e+300\n",
      "  173    1.0e+165      127     5.2e+135    5.3e+300\n",
      "  174    3.9e+165      126     1.1e+135    4.1e+300\n",
      "  175    1.5e+166      125     2.1e+134    3.2e+300\n",
      "  176    5.8e+166      124     4.3e+133    2.5e+300\n",
      "  177    2.2e+167      123     8.5e+132    1.9e+300\n",
      "  178    8.4e+167      122     1.7e+132    1.4e+300\n",
      "  179    3.2e+168      121     3.3e+131    1.1e+300\n",
      "  180    1.2e+169      120     6.5e+130    7.7e+299\n",
      "  181    4.5e+169      119     1.3e+130    5.6e+299\n",
      "  182    1.7e+170      118     2.4e+129    4.1e+299\n",
      "  183    6.3e+170      117     4.6e+128    2.9e+299\n",
      "  184    2.3e+171      116     8.8e+127    2.0e+299\n",
      "  185    8.6e+171      115     1.7e+127    1.4e+299\n",
      "  186    3.2e+172      114     3.1e+126    9.8e+298\n",
      "  187    1.2e+173      113     5.8e+125    6.7e+298\n",
      "  188    4.3e+173      112     1.1e+125    4.5e+298\n",
      "  189    1.5e+174      111     1.9e+124    3.0e+298\n",
      "  190    5.6e+174      110     3.5e+123    2.0e+298\n",
      "  191    2.0e+175      109     6.4e+122    1.3e+298\n",
      "  192    7.3e+175      108     1.1e+122    8.4e+297\n",
      "  193    2.6e+176      107     2.0e+121    5.3e+297\n",
      "  194    9.3e+176      106     3.6e+120    3.4e+297\n",
      "  195    3.3e+177      105     6.3e+119    2.1e+297\n",
      "  196    1.2e+178      104     1.1e+119    1.3e+297\n",
      "  197    4.2e+178      103     1.9e+118    7.9e+296\n",
      "  198    1.5e+179      102     3.2e+117    4.8e+296\n",
      "  199    5.1e+179      101     5.5e+116    2.8e+296\n",
      "  200    1.8e+180      100     9.3e+115    1.7e+296\n",
      "  201    6.3e+180       99     1.5e+115    9.7e+295\n",
      "  202    2.2e+181       98     2.6e+114    5.6e+295\n",
      "  203    7.5e+181       97     4.2e+113    3.2e+295\n",
      "  204    2.6e+182       96     6.8e+112    1.8e+295\n",
      "  205    8.9e+182       95     1.1e+112    9.8e+294\n",
      "  206    3.0e+183       94     1.8e+111    5.4e+294\n",
      "  207    1.0e+184       93     2.8e+110    2.9e+294\n",
      "  208    3.5e+184       92     4.4e+109    1.6e+294\n",
      "  209    1.2e+185       91     6.8e+108    8.2e+293\n",
      "  210    4.0e+185       90     1.1e+108    4.3e+293\n",
      "  211    1.4e+186       89     1.6e+107    2.2e+293\n",
      "  212    4.6e+186       88     2.4e+106    1.1e+293\n",
      "  213    1.5e+187       87     3.7e+105    5.6e+292\n",
      "  214    5.1e+187       86     5.4e+104    2.8e+292\n",
      "  215    1.7e+188       85     8.0e+103    1.3e+292\n",
      "  216    5.6e+188       84     1.2e+103    6.5e+291\n",
      "  217    1.8e+189       83     1.7e+102    3.1e+291\n",
      "  218    6.0e+189       82     2.4e+101    1.4e+291\n",
      "  219    2.0e+190       81     3.4e+100    6.7e+290\n",
      "  220    6.5e+190       80     4.7e+99    3.1e+290\n",
      "  221    2.1e+191       79     6.5e+98    1.4e+290\n",
      "  222    6.9e+191       78     8.9e+97    6.1e+289\n",
      "  223    2.2e+192       77     1.2e+97    2.7e+289\n",
      "  224    7.2e+192       76     1.6e+96    1.2e+289\n",
      "  225    2.3e+193       75     2.1e+95    4.9e+288\n",
      "  226    7.4e+193       74     2.8e+94    2.1e+288\n",
      "  227    2.4e+194       73     3.6e+93    8.5e+287\n",
      "  228    7.5e+194       72     4.6e+92    3.4e+287\n",
      "  229    2.4e+195       71     5.8e+91    1.4e+287\n",
      "  230    7.6e+195       70     7.2e+90    5.5e+286\n",
      "  231    2.4e+196       69     8.8e+89    2.1e+286\n",
      "  232    7.6e+196       68     1.1e+89    8.1e+285\n",
      "  233    2.4e+197       67     1.3e+88    3.1e+285\n",
      "  234    7.5e+197       66     1.5e+87    1.1e+285\n",
      "  235    2.3e+198       65     1.8e+86    4.1e+284\n",
      "  236    7.2e+198       64     2.1e+85    1.5e+284\n",
      "  237    2.3e+199       63     2.3e+84    5.2e+283\n",
      "  238    7.0e+199       62     2.6e+83    1.8e+283\n",
      "  239    2.2e+200       61     2.9e+82    6.2e+282\n",
      "  240    6.6e+200       60     3.1e+81    2.1e+282\n",
      "  241    2.0e+201       59     3.4e+80    6.9e+281\n",
      "  242    6.2e+201       58     3.6e+79    2.2e+281\n",
      "  243    1.9e+202       57     3.7e+78    7.1e+280\n",
      "  244    5.8e+202       56     3.8e+77    2.2e+280\n",
      "  245    1.8e+203       55     3.8e+76    6.8e+279\n",
      "  246    5.3e+203       54     3.8e+75    2.0e+279\n",
      "  247    1.6e+204       53     3.7e+74    6.0e+278\n",
      "  248    4.8e+204       52     3.6e+73    1.7e+278\n",
      "  249    1.5e+205       51     3.4e+72    4.9e+277\n",
      "  250    4.4e+205       50     3.1e+71    1.4e+277\n",
      "  251    1.3e+206       49     2.9e+70    3.7e+276\n",
      "  252    3.9e+206       48     2.6e+69    9.9e+275\n",
      "  253    1.2e+207       47     2.2e+68    2.6e+275\n",
      "  254    3.4e+207       46     1.9e+67    6.6e+274\n",
      "  255    1.0e+208       45     1.6e+66    1.6e+274\n",
      "  256    3.0e+208       44     1.3e+65    4.0e+273\n",
      "  257    8.8e+208       43     1.1e+64    9.6e+272\n",
      "  258    2.6e+209       42     8.7e+62    2.2e+272\n",
      "  259    7.5e+209       41     6.7e+61    5.1e+271\n",
      "  260    2.2e+210       40     5.1e+60    1.1e+271\n",
      "  261    6.4e+210       39     3.8e+59    2.4e+270\n",
      "  262    1.9e+211       38     2.7e+58    5.1e+269\n",
      "  263    5.4e+211       37     1.9e+57    1.0e+269\n",
      "  264    1.6e+212       36     1.3e+56    2.1e+268\n",
      "  265    4.5e+212       35     9.0e+54    4.1e+267\n",
      "  266    1.3e+213       34     5.9e+53    7.6e+266\n",
      "  267    3.7e+213       33     3.8e+52    1.4e+266\n",
      "  268    1.1e+214       32     2.3e+51    2.5e+265\n",
      "  269    3.0e+214       31     1.4e+50    4.3e+264\n",
      "  270    8.6e+214       30     8.2e+48    7.1e+263\n",
      "  271    2.5e+215       29     4.7e+47    1.1e+263\n",
      "  272    6.9e+215       28     2.6e+46    1.8e+262\n",
      "  273    2.0e+216       27     1.4e+45    2.7e+261\n",
      "  274    5.5e+216       26     7.0e+43    3.9e+260\n",
      "  275    1.6e+217       25     3.5e+42    5.4e+259\n",
      "  276    4.4e+217       24     1.7e+41    7.2e+258\n",
      "  277    1.2e+218       23     7.6e+39    9.3e+257\n",
      "  278    3.4e+218       22     3.3e+38    1.1e+257\n",
      "  279    9.6e+218       21     1.4e+37    1.4e+256\n",
      "  280    2.7e+219       20     5.7e+35    1.5e+255\n",
      "  281    7.4e+219       19     2.2e+34    1.6e+254\n",
      "  282    2.0e+220       18     8.1e+32    1.6e+253\n",
      "  283    5.7e+220       17     2.8e+31    1.6e+252\n",
      "  284    1.6e+221       16     9.2e+29    1.4e+251\n",
      "  285    4.3e+221       15     2.9e+28    1.2e+250\n",
      "  286    1.2e+222       14     8.4e+26    9.9e+248\n",
      "  287    3.2e+222       13     2.3e+25    7.4e+247\n",
      "  288    8.8e+222       12     5.8e+23    5.1e+246\n",
      "  289    2.4e+223       11     1.4e+22    3.3e+245\n",
      "  290    6.5e+223       10     2.9e+20    1.9e+244\n",
      "  291    1.8e+224        9     5.8e+18    1.0e+243\n",
      "  292    4.8e+224        8     1.0e+17    4.9e+241\n",
      "  293    1.3e+225        7     1.6e+15    2.1e+240\n",
      "  294    3.5e+225        6     2.2e+13    7.8e+238\n",
      "  295    9.4e+225        5     2.7e+11    2.5e+237\n",
      "  296    2.5e+226        4     2.6e+09    6.7e+235\n",
      "  297    6.8e+226        3     2.1e+07    1.4e+234\n",
      "  298    1.8e+227        2      125250    2.3e+232\n",
      "  299    4.8e+227        1         500    2.4e+230\n",
      "  300    1.3e+228        0           1    1.3e+228\n",
      "Total microstates =  2.0e+303\n"
     ]
    }
   ],
   "source": [
    "Omega_tot_array = macrostate_table(500, 500, 300, table=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9f60e675",
   "metadata": {},
   "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(Omega_tot_array))\n",
    "ax0.plot(q_array, Omega_tot_array, color='blue')\n",
    "ax0.fill_between(q_array, Omega_tot_array, color='lightblue')\n",
    "ax0.set_xlabel(r'$q_A$')\n",
    "ax0.set_ylabel(r'total multiplicity $\\Omega_{\\rm total}$')\n",
    "ax0.set_xlim(q_array[0], q_array[-1])\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "036c48e0",
   "metadata": {},
   "outputs": [
    {
     "ename": "OverflowError",
     "evalue": "int too large to convert to float",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mOverflowError\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[16], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m Omega_tot_array \u001b[38;5;241m=\u001b[39m \u001b[43mmacrostate_table\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m600\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m500\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m300\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtable\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[0;32mIn[8], line 25\u001b[0m, in \u001b[0;36mmacrostate_table\u001b[0;34m(N_A, N_B, q_tot, table)\u001b[0m\n\u001b[1;32m     22\u001b[0m Omega_B \u001b[38;5;241m=\u001b[39m ein_mult(N_B, q_B) \n\u001b[1;32m     24\u001b[0m Omega_tot \u001b[38;5;241m=\u001b[39m Omega_A \u001b[38;5;241m*\u001b[39m Omega_B\n\u001b[0;32m---> 25\u001b[0m Omega_tot_array[q_A] \u001b[38;5;241m=\u001b[39m Omega_tot\n\u001b[1;32m     26\u001b[0m tot_microstates \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m Omega_tot\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m table:\n",
      "\u001b[0;31mOverflowError\u001b[0m: int too large to convert to float"
     ]
    }
   ],
   "source": [
    "Omega_tot_array = macrostate_table(600, 500, 300, table=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cbf4094e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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