  Putting the point in more modern terms, the laws of (Hamiltonian) mechanics are such that for every solution one can construct another solution by reversing all velocities and replacing \(t\) by \(-t\). Since \(H[f]\) is invariant under the velocity reversal, it follows that if \(H[f]\) decreases for the first solution, it will increase for the second. Accordingly, the reversibility objection is that the H-theorem cannot be a general theorem for all mechanical evolutions of the gas.