composite-system-entropy.py

import matplotlib.pyplot as plt
import numpy as np

from math import comb, log

def annotate_max(x, y, ax=None):
    xmax = x[np.argmax(y)]
    ymax = y.max()
    text= "U_A={:.3f}, S={:.3f}".format(xmax, ymax)
    if not ax:
        ax=plt.gca()
    bbox_props = dict(boxstyle="square,pad=0.3", fc="w", ec="k", lw=0.72)
    arrowprops=dict(arrowstyle="->",connectionstyle="angle,angleA=0,angleB=60")
    kw = dict(xycoords='data',textcoords="axes fraction",
              arrowprops=arrowprops, bbox=bbox_props, ha="right", va="top")
    ax.annotate(text, xy=(xmax, ymax), xytext=(0.94,0.96), **kw)

U_Amax = 100
U_Bmax = 60

U_t = 30

U = np.arange(0, U_t + 1)

S_A = np.zeros(U_t + 1)
S_B = np.zeros(U_t + 1)

for U_A in range(0, U_t + 1):
    S_A[U_A] = log(comb(U_Amax, U_A))
    S_B[U_A] = log(comb(U_Bmax, U_t - U_A))

S = S_A + S_B

plt.plot(U, S_A)
plt.plot(U, S_B)
plt.plot(U, S)

annotate_max(U, S)

plt.legend(['S_A', 'S_B', 'S'])
plt.title('S vs. U_A')
plt.xlabel('U_A')
plt.ylabel('S')

plt.show()