diff --git a/docs/source/manual/advanced_usage.rst b/docs/source/manual/advanced_usage.rst
index b3e0c151..c2569d3c 100644
--- a/docs/source/manual/advanced_usage.rst
+++ b/docs/source/manual/advanced_usage.rst
@@ -207,7 +207,7 @@ A simple implementation for the Kuramoto–Sivashinsky equation could read
     class KuramotoSivashinskyPDE(PDEBase):
 
         def evolution_rate(self, state, t=0):
-            """ numpy implementation of the evolution equation """
+            """Evaluate the right hand side of the evolution equation."""
             state_lapacian = state.laplace(bc="auto_periodic_neumann")
             state_gradient = state.gradient(bc="auto_periodic_neumann")
             return (- state_lapacian.laplace(bc="auto_periodic_neumann")
@@ -222,14 +222,13 @@ instance define the boundary conditions and the diffusivity:
     class KuramotoSivashinskyPDE(PDEBase):
 
         def __init__(self, diffusivity=1, bc="auto_periodic_neumann", bc_laplace="auto_periodic_neumann"):
-            """ initialize the class with a diffusivity and boundary conditions
-            for the actual field and its second derivative """
+            """Initialize the class with a diffusivity and boundary conditions."""
             self.diffusivity = diffusivity
             self.bc = bc
             self.bc_laplace = bc_laplace
 
         def evolution_rate(self, state, t=0):
-            """ numpy implementation of the evolution equation """
+            """Evaluate the right hand side of the evolution equation."""
             state_lapacian = state.laplace(bc=self.bc)
             state_gradient = state.gradient(bc=self.bc)
             return (- state_lapacian.laplace(bc=self.bc_laplace)
@@ -245,6 +244,37 @@ While such an implementation is helpful for testing initial ideas, actual
 computations should be performed with compiled PDEs as described below.
 
 
+Another feature of custom PDE classes are a special function that is called after every
+time step. This function allows direct manipulation of the state data and also abortion
+of the simulation by raising :class:`StopIteration`.
+
+.. code-block:: python
+
+    class AbortEarlyPDE(PDEBase):
+
+        def make_post_step_hook(self, state):
+            """Create a hook function that is called after every time step."""
+
+            def post_step_hook(state_data, t):
+                """Limit state to [-1, 1] & abort when standard deviation exceeds 1."""
+                np.clip(state_data, -1, 1, out=state_data)  # limit state
+                if state_data.std() > 1:
+                    raise StopIteration  # abort simulation
+                return 1  # count the number of times the hook was called
+
+            return post_step_hook
+
+        def evolution_rate(self, state, t=0):
+            """Evaluate the right hand side of the evolution equation."""
+            return state
+
+We here use a simple constant evolution equation. The hook defined by the first method
+does two things: First, it limits the state to the interval `[-1, 1]` using
+:func:`numpy.clip`. Second, it evaluates the standard deviation across the entire data,
+aborting the simulation when the value exceeds one. Note that the hook always receives
+the data always as a :class:`~numpy.ndarray` and not as a full field class.
+
+
 Low-level operators
 """""""""""""""""""
 This section explains how to use the low-level version of the field operators.
diff --git a/pde/pdes/base.py b/pde/pdes/base.py
index e26ec59e..dd7de0ee 100644
--- a/pde/pdes/base.py
+++ b/pde/pdes/base.py
@@ -16,7 +16,7 @@
 from ..fields.base import FieldBase
 from ..fields.datafield_base import DataFieldBase
 from ..tools.numba import jit
-from ..tools.typing import ArrayLike
+from ..tools.typing import ArrayLike, StepperHook
 from ..trackers.base import TrackerCollectionDataType
 
 if TYPE_CHECKING:
@@ -110,14 +110,14 @@ def is_sde(self) -> bool:
         # check for self.noise, in case __init__ is not called in a subclass
         return hasattr(self, "noise") and np.any(self.noise != 0)  # type: ignore
 
-    def make_post_step_hook(self, state: FieldBase) -> Callable[[np.ndarray], float]:
+    def make_post_step_hook(self, state: FieldBase) -> StepperHook:
         """Returns a function that is called after each step.
 
-        This function receives the current state as a numpy array and can modify the
-        data in place. The function must return a float value, which normally indicates
-        how much the state was modified. This value does not affect the simulation, but
-        is accumulated over time and provided in the diagnostic information for
-        debugging.
+        This function receives the current state as a numpy array together with the
+        current time point. The function can modify the state data in place. The
+        function must return a float value, which normally indicates how much the state
+        was modified. This value does not affect the simulation, but is accumulated over
+        time and provided in the diagnostic information for debugging.
 
         The hook can also be used to abort the simulation when a user-defined condition
         is met by raising `StopIteration`. Note that this interrupts the inner-most loop
@@ -135,7 +135,7 @@ def make_post_step_hook(self, state: FieldBase) -> Callable[[np.ndarray], float]
             measure for the corrections applied to the state
         """
 
-        def post_step_hook(state_data: np.ndarray) -> float:
+        def post_step_hook(state_data: np.ndarray, t: float) -> float:
             """No-op function."""
             return 0
 
diff --git a/pde/solvers/adams_bashforth.py b/pde/solvers/adams_bashforth.py
index 072f11bc..ec9badcd 100644
--- a/pde/solvers/adams_bashforth.py
+++ b/pde/solvers/adams_bashforth.py
@@ -71,7 +71,7 @@ def fixed_stepper(
                 # calculate the right hand side
                 t = t_start + i * dt
                 single_step(state_data, t, state_prev)
-                modifications += post_step_hook(state_data)
+                modifications += post_step_hook(state_data, t)
 
             return t + dt, modifications
 
diff --git a/pde/solvers/base.py b/pde/solvers/base.py
index 2145aee3..9e224c90 100644
--- a/pde/solvers/base.py
+++ b/pde/solvers/base.py
@@ -23,7 +23,7 @@
 from ..tools.math import OnlineStatistics
 from ..tools.misc import classproperty
 from ..tools.numba import is_jitted, jit
-from ..tools.typing import BackendType
+from ..tools.typing import BackendType, StepperHook
 
 
 class ConvergenceError(RuntimeError):
@@ -119,7 +119,7 @@ def _compiled(self) -> bool:
             self.backend == "numba" and not nb.config.DISABLE_JIT
         )  # @UndefinedVariable
 
-    def _make_post_step_hook(self, state: FieldBase) -> Callable[[np.ndarray], float]:
+    def _make_post_step_hook(self, state: FieldBase) -> StepperHook:
         """Create a function that modifies a state after each step.
 
         A noop function will be returned if `_post_step_hook` is `False`,
@@ -133,23 +133,31 @@ def _make_post_step_hook(self, state: FieldBase) -> Callable[[np.ndarray], float
             if hasattr(self.pde, "make_modify_after_step"):
                 # Deprecated on 2024-08-02
                 warnings.warn(
-                    "`make_modify_after_step` has been renamed to `make_post_step_hook`",
+                    "`make_modify_after_step` has been replaced by `make_post_step_hook`",
                     DeprecationWarning,
                 )
-                post_step_hook = jit(self.pde.make_modify_after_step(state))
+                modify_after_step = self.pde.make_modify_after_step(state)
+                if self._compiled:
+                    sig_modify = (nb.typeof(state.data),)
+                    modify_after_step = jit(sig_modify)(modify_after_step)
+
+                def post_step_hook(state_data: np.ndarray, t: float) -> float:
+                    """Wrap function to adjust signature."""
+                    return modify_after_step(state_data)  # type: ignore
+
             else:
-                post_step_hook = jit(self.pde.make_post_step_hook(state))
+                post_step_hook = self.pde.make_post_step_hook(state)
 
         else:
 
-            def post_step_hook(state_data: np.ndarray) -> float:
-                return 0
+            def post_step_hook(state_data: np.ndarray, t: float) -> float:
+                return 0.0
 
         if self._compiled:
-            sig_modify = (nb.typeof(state.data),)
-            post_step_hook = jit(sig_modify)(post_step_hook)
+            sig_hook = (nb.typeof(state.data), nb.float64)
+            post_step_hook = jit(sig_hook)(post_step_hook)
 
-        return post_step_hook  # type: ignore
+        return post_step_hook
 
     def _make_pde_rhs(
         self, state: FieldBase, backend: BackendType = "auto"
@@ -266,7 +274,7 @@ def fixed_stepper(
                 # calculate the right hand side
                 t = t_start + i * dt
                 single_step(state_data, t)
-                modifications += post_step_hook(state_data)
+                modifications += post_step_hook(state_data, t)
 
             return t + dt, modifications
 
@@ -538,7 +546,7 @@ def adaptive_stepper(
                     steps += 1
                     t += dt_step
                     state_data[...] = new_state
-                    modifications += post_step_hook(state_data)
+                    modifications += post_step_hook(state_data, t)
                     if dt_stats is not None:
                         dt_stats.add(dt_step)
 
diff --git a/pde/solvers/explicit.py b/pde/solvers/explicit.py
index d575a5ba..567522f7 100644
--- a/pde/solvers/explicit.py
+++ b/pde/solvers/explicit.py
@@ -240,7 +240,7 @@ def adaptive_stepper(
                         steps += 1
                         t += dt_step
                         state_data[...] = step_small
-                        modifications += post_step_hook(state_data)
+                        modifications += post_step_hook(state_data, t)
                         if dt_stats is not None:
                             dt_stats.add(dt_step)
 
diff --git a/pde/tools/typing.py b/pde/tools/typing.py
index 7ea328ed..253dde8a 100644
--- a/pde/tools/typing.py
+++ b/pde/tools/typing.py
@@ -54,3 +54,8 @@ def __call__(
 class GhostCellSetter(Protocol):
     def __call__(self, data_full: np.ndarray, args=None) -> None:
         """Set the ghost cells."""
+
+
+class StepperHook(Protocol):
+    def __call__(self, state_data: np.ndarray, t: float) -> float:
+        """Function analyzing and potentially modifying the current state."""
diff --git a/tests/test_integration.py b/tests/test_integration.py
index 3c7792ca..654b5245 100644
--- a/tests/test_integration.py
+++ b/tests/test_integration.py
@@ -134,7 +134,7 @@ def test_stop_iteration_hook(backend):
 
     class TestPDE(PDEBase):
         def make_post_step_hook(self, state):
-            def post_step_hook(state_data):
+            def post_step_hook(state_data, t):
                 if state_data.sum() > 1:
                     raise StopIteration
                 return 1  # count the number of times the hook was called