diff --git a/chiron/tests/test_multistate.py b/chiron/tests/test_multistate.py
index 23155db..4125eeb 100644
--- a/chiron/tests/test_multistate.py
+++ b/chiron/tests/test_multistate.py
@@ -5,10 +5,10 @@
 @pytest.fixture
 def ho_multistate_sampler() -> MultiStateSampler:
     """
-    Create a MultiStateSampler object for performing multistate simulations for a harmonic oscillator.
+    Create a multi-state sampler for a harmonic oscillator system.
 
     Returns:
-        MultiStateSampler: The created MultiStateSampler object.
+        MultiStateSampler: The multi-state sampler object.
     """
     import math
     from openmm import unit
@@ -29,10 +29,17 @@ def ho_multistate_sampler() -> MultiStateSampler:
         / (math.e - 1.0)
         for i in range(n_replicas)
     ]
+    import jax.numpy as jnp
 
-    ho_potential = HarmonicOscillatorPotential(ho.topology)
+    x0s = [
+        unit.Quantity(jnp.array([[x0, 0.0, 0.0]]), unit.angstrom)
+        for x0 in jnp.linspace(0.0, 1.0, n_replicas)
+    ]
     thermodynamic_states = [
-        ThermodynamicState(ho_potential, temperature=T) for T in temperatures
+        ThermodynamicState(
+            HarmonicOscillatorPotential(ho.topology, x0=x0), temperature=T
+        )
+        for T, x0 in zip(temperatures, x0s)
     ]
     sampler_state = [SamplerState(ho.positions) for _ in temperatures]
 
@@ -68,4 +75,21 @@ def test_multistate_class(ho_multistate_sampler):
 
 
 def test_multistate_minimize(ho_multistate_sampler):
+    """
+    Test function for the `minimize` method of the `ho_multistate_sampler` object.
+    It checks if the sampler states are correctly minimized.
+
+    Parameters
+    ----------
+    ho_multistate_sampler: The `ho_multistate_sampler` object to be tested.
+    """
+
+    import numpy as np
+
     ho_multistate_sampler.minimize()
+
+    assert np.allclose(
+        ho_multistate_sampler.sampler_states[0].x0, np.array([[0.0, 0.0, 0.0]])
+    )
+    assert np.allclose(ho_multistate_sampler.sampler_states[1].x0, np.array([[0.05, 0.0, 0.0]]), atol=1e-2)
+    assert np.allclose(ho_multistate_sampler.sampler_states[2].x0, np.array([[0.1, 0.0, 0.0]]), atol=1e-2)