diff --git a/docs/src/overview.md b/docs/src/overview.md
index b81cd0c0..2966d83a 100644
--- a/docs/src/overview.md
+++ b/docs/src/overview.md
@@ -33,6 +33,18 @@ Several equation systems in [DispersiveShallowWater.jl](https://github.com/Numer
 
 The common interface provides shared functionality like [`waterheight`](@ref), [`velocity`](@ref), [`energy_total`](@ref), and [`entropy`](@ref). This enables consistent analysis and visualization across different dispersive models while maintaining the underlying shallow water physics.
 
+!!! warning "Entropy vs. Energy"
+    [DispersiveShallowWater.jl](https://github.com/NumericalMathematics/DispersiveShallowWater.jl)
+    is written by mathematicians with a background in numerical methods for
+    hyperbolic balance laws. Therefore, the term *entropy* is often used
+    in the sense of a mathematical entropy function, i.e., typically a
+    convex function that is conserved by smooth solutions and whose dissipation
+    provides useful bounds and estimates. For the classical shallow water
+    equations, the mathematical entropy is the same as the physical energy
+    (see [`energy_total`](@ref) and [`entropy`](@ref)). However, some dispersive
+    models like the [`SerreGreenNaghdiEquations1D`](@ref) do not conserve
+    the [`energy_total`](@ref) but a modified form [`energy_total_modified`](@ref).
+
 ## Hyperbolic Approximations
 
 Some equations are hyperbolic approximations of other systems (e.g., [`HyperbolicSerreGreenNaghdiEquations1D`](@ref) approximates [`SerreGreenNaghdiEquations1D`](@ref)). These systems support two approaches for initial conditions:
diff --git a/src/equations/equations.jl b/src/equations/equations.jl
index 82b85e58..cebe699f 100644
--- a/src/equations/equations.jl
+++ b/src/equations/equations.jl
@@ -294,7 +294,7 @@ varnames(::typeof(energy_total), equations) = ("e_total",)
 """
     entropy(q, equations)
 
-Return the entropy ``U`` of the primitive variables `q` for a given set of
+Return the mathematical entropy ``U`` of the primitive variables `q` for a given set of
 `equations`. For all [`AbstractShallowWaterEquations`](@ref), the `entropy`
 is just the [`energy_total`](@ref).
 
diff --git a/src/equations/kdv_1d.jl b/src/equations/kdv_1d.jl
index 301fd9f4..bb9e6ca3 100644
--- a/src/equations/kdv_1d.jl
+++ b/src/equations/kdv_1d.jl
@@ -299,7 +299,7 @@ end
 """
     entropy(q, equations::KdVEquation1D)
 
-Return the entropy ``U`` of the primitive variables `q` for the [`KdVEquation1D`](@ref).
+Return the mathematical entropy ``U`` of the primitive variables `q` for the [`KdVEquation1D`](@ref).
 For the KdV equation, the `entropy` is the same as the [`energy_total`](@ref).
 
 `q` is a vector of the primitive variables at a single node, i.e., a vector