problem3.24.ipynb

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    "%matplotlib widget"
   ]
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  {
   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.special as sp"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
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   "source": [
    "def factorial(x):\n",
    "    return sp.factorial(x, exact=True)\n",
    "\n",
    "def multiplicityEinstein(N,q):\n",
    "    return factorial(q+N-1)//factorial(q)//factorial(N-1)\n",
    "\n",
    "def logArray(array):\n",
    "    import math as math\n",
    "    return [math.log(x) for x in array]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'q': range(101)})\n",
    "\n",
    "N = 50\n",
    "\n",
    "df['multiplicity'] = multiplicityEinstein(N, df['q'])\n",
    "\n",
    "df['S/k'] = logArray(df['multiplicity'])\n",
    "\n",
    "df['kT/e'] = (np.gradient(df['S/k'])/np.gradient(df['q']))**-1\n",
    "\n",
    "df['C/Nk'] = np.gradient(df['q'])/np.gradient(df['kT/e'])/N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
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       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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     "metadata": {},
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     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='q'>"
      ]
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   "source": [
    "df.plot(x='q', y='S/k', marker='.', linestyle='none')"
   ]
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       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='kT/e'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
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   ],
   "source": [
    "df.plot(x='kT/e', y='C/Nk', marker='.', linestyle='none')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'q': range(101)})\n",
    "\n",
    "N = 5000\n",
    "\n",
    "df['multiplicity']=multiplicityEinstein(N, df['q'])\n",
    "\n",
    "df['S/k']=logArray(df['multiplicity'])\n",
    "\n",
    "df['kT/e'] = (np.gradient(df['S/k'])/np.gradient(df['q']))**-1\n",
    "\n",
    "df['C/Nk'] = np.gradient(df['q'])/np.gradient(df['kT/e'])/N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
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     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='q'>"
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     "execution_count": 20,
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   "source": [
    "df.plot(x='q', y='S/k', marker='.', linestyle='none')"
   ]
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     "data": {
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       "<AxesSubplot:xlabel='kT/e'>"
      ]
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     "execution_count": 21,
     "metadata": {},
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   "source": [
    "df.plot(x='kT/e', y='C/Nk', marker='.', linestyle='none')"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   "execution_count": null,
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