diff --git a/DIRECTORY.md b/DIRECTORY.md
index 150e4e61ea06..38a7df0737e5 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -986,6 +986,7 @@
   * [Doppler Frequency](physics/doppler_frequency.py)
   * [Escape Velocity](physics/escape_velocity.py)
   * [Grahams Law](physics/grahams_law.py)
+  * [Hamiltonian](physics/hamiltonian.py)
   * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py)
   * [Hubble Parameter](physics/hubble_parameter.py)
   * [Ideal Gas Law](physics/ideal_gas_law.py)
@@ -1404,6 +1405,7 @@
   * [Selection Sort](sorts/selection_sort.py)
   * [Shell Sort](sorts/shell_sort.py)
   * [Shrink Shell Sort](sorts/shrink_shell_sort.py)
+  * [Sleep Sort](sorts/sleep_sort.py)
   * [Slowsort](sorts/slowsort.py)
   * [Smoothsort](sorts/smoothsort.py)
   * [Stalin Sort](sorts/stalin_sort.py)
diff --git a/sorts/sleep_sort.py b/sorts/sleep_sort.py
new file mode 100644
index 000000000000..cf38a3e017c0
--- /dev/null
+++ b/sorts/sleep_sort.py
@@ -0,0 +1,40 @@
+import threading
+import time
+
+
+def sleep_sort(arr):
+    """
+    Sorts a list of positive integers using Sleep Sort.
+
+    Args:
+        arr (list[int]): List of positive integers to sort.
+
+    Returns:
+        list[int]: Sorted list in ascending order.
+    """
+    result = []
+
+    def sleeper(x):
+        # Sleep for a duration proportional to the number
+        time.sleep(x * 0.01)  # scale down to avoid long delays
+        result.append(x)
+
+    threads = [threading.Thread(target=sleeper, args=(num,)) for num in arr]
+
+    # Start all threads
+    for t in threads:
+        t.start()
+
+    # Wait for all threads to finish
+    for t in threads:
+        t.join()
+
+    return result
+
+
+# Example Usage
+if __name__ == "__main__":
+    numbers = [4, 1, 3, 2]
+    sorted_numbers = sleep_sort(numbers)
+    print("Original:", numbers)
+    print("Sorted:", sorted_numbers)