Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell in 1867 in which he suggested how the second law of thermodynamics might hypothetically be violated.[1] In the thought experiment, a demon controls a small door between two chambers of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing entropy and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and information theory extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.
Maxwell's Demon
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import numpy as np
import matplotlib.pyplot as plt
from celluloid import Camera
# DEFINE FIXED VALUES
# Set how many periods you'd like to run your world
PERIOD_MAX = 1000
# Set the boundaries of the box
BOUND_X_MIN = -15
BOUND_X_MAX = 15
BOUND_Y_MIN = -15
BOUND_Y_MAX = 15
# GATE
GATE_X = 0
#GATE_Y_MIN = -2
#GATE_Y_MAX = 2
# SPEED TYPES
SLOW = 0.2
FAST = 1
# Initial positions
INITIAL_PARTICLE_POSITIONS_X = np.array([6, 5, -3, -8])
INITIAL_PARTICLE_POSITIONS_Y = np.array([4, 20, -15, -11])
# Initial speed
INITIAL_PARTICLE_SPEEDS = np.array([SLOW, FAST, SLOW, FAST])
# Initial Velocity direction as unit vectors
INITIAL_PARTICLE_DIRECTIONS_X = np.array([-np.sqrt(2) / 2, 1, np.sqrt(3)/2, 0.6])
INITIAL_PARTICLE_DIRECTIONS_Y = np.array([-np.sqrt(2) / 2, 0, 1/2, 0.8])
# Total number of particles
particle_total_number = len(INITIAL_PARTICLE_POSITIONS_X)
# Create System State Matrix by defining the correct dimensions
system_state_matrix = np.ndarray(shape=(PERIOD_MAX + 1, 5, particle_total_number))
# Initialize the first entry of the state matrix with the initial values
system_state_matrix[0] = \
INITIAL_PARTICLE_POSITIONS_X, INITIAL_PARTICLE_POSITIONS_Y, INITIAL_PARTICLE_SPEEDS, INITIAL_PARTICLE_DIRECTIONS_X, \
INITIAL_PARTICLE_DIRECTIONS_Y
# Now let's make the particles move
# The Loop to update system
for i in np.arange(0, PERIOD_MAX):
# At each loop, system will move from t=i to t=i+1
# first get the "old" values at t=i
# 2 dimensional position array
particle_positions_at_i = system_state_matrix[i][0:2]
# 1 dimensional speed array
particle_speeds_at_i = system_state_matrix[i][2]
# 2 dimensional velocity direction array
particle_directions_at_i = system_state_matrix[i][3:5]
# First calculate as if no boundary
particle_positions_temporary_array = particle_positions_at_i + particle_speeds_at_i * particle_directions_at_i
# Initialize the next period vectors temporarily
particle_positions_at_i_plus_one = particle_positions_temporary_array
# Make a deep copy to prevent wrong value updating
particle_directions_at_i_plus_one = particle_directions_at_i.copy()
# Now check the boundary conditions and make the necessary updates
# Vertical bounds:
positions_x_out_of_bounds_right = (particle_positions_temporary_array[0] > BOUND_X_MAX)
positions_x_out_of_bounds_left = (particle_positions_temporary_array[0] < BOUND_X_MIN)
positions_x_all_out_of_bound_vertical= np.logical_or(positions_x_out_of_bounds_right, positions_x_out_of_bounds_left)
particle_directions_at_i_plus_one[0][positions_x_all_out_of_bound_vertical] *= -1
particle_positions_at_i_plus_one[0][positions_x_out_of_bounds_right] = 2 * BOUND_X_MAX - \
particle_positions_at_i_plus_one[0][
positions_x_out_of_bounds_right]
particle_positions_at_i_plus_one[0][positions_x_out_of_bounds_left] = 2 * BOUND_X_MIN - \
particle_positions_at_i_plus_one[0][
positions_x_out_of_bounds_left]
# Horizontal bounds
positions_y_out_of_bounds_up = (particle_positions_temporary_array[1] > BOUND_Y_MAX)
positions_x_out_of_bounds_down = (particle_positions_temporary_array[1] < BOUND_X_MIN)
particle_directions_at_i_plus_one[1][
np.logical_or(positions_y_out_of_bounds_up, positions_x_out_of_bounds_down)] *= -1
particle_positions_at_i_plus_one[1][positions_y_out_of_bounds_up] = 2 * BOUND_Y_MAX - \
particle_positions_at_i_plus_one[1][
positions_y_out_of_bounds_up]
particle_positions_at_i_plus_one[1][positions_x_out_of_bounds_down] = 2 * BOUND_Y_MIN - \
particle_positions_at_i_plus_one[1][
positions_x_out_of_bounds_down]
# Check Gate conditions
gate_blocking_left_to_right = np.logical_and.reduce((particle_positions_at_i[0] <= GATE_X,
particle_positions_at_i_plus_one[0] > GATE_X,
particle_speeds_at_i == SLOW))
gate_blocking_right_to_left = np.logical_and.reduce((particle_positions_at_i[0] >= GATE_X,
particle_positions_at_i_plus_one[0] < GATE_X,
particle_speeds_at_i == FAST))
gate_bouncers = np.logical_or(gate_blocking_left_to_right, gate_blocking_right_to_left)
particle_positions_at_i_plus_one[0][gate_bouncers] = 2 * GATE_X - particle_positions_at_i_plus_one[0][gate_bouncers]
particle_directions_at_i_plus_one[0][gate_bouncers] *= -1
# Write the finalized data to the state matrix
system_state_matrix[i + 1] = particle_positions_at_i_plus_one[0], particle_positions_at_i_plus_one[
1], particle_speeds_at_i, particle_directions_at_i_plus_one[0], particle_directions_at_i_plus_one[1]
# Collect the data
print(system_state_matrix)
# Plotting
fig = plt.figure()
camera = Camera(fig)
plt.axis([BOUND_X_MIN, BOUND_X_MAX, BOUND_Y_MIN, BOUND_Y_MAX])
for i in np.arange(0, PERIOD_MAX):
X = system_state_matrix[i][0]
Y = system_state_matrix[i][1]
Z = system_state_matrix[i][2]
plt.scatter(X, Y, c=Z,cmap='bwr')
camera.snap()
animation = camera.animate()
animation.save('ozgun_demon.html')
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