Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any insights into what breaks the symmetry between real time and the mathematical description?
Actually, it's not true that our laws of physics are symmetric under time reversal. The Standard Model of particle physics isn't.
In fact, it's been strongly suspected since the 1960s that the laws of physics can't be invariant under the operation of time reversal. There is a very reliable theoretical result called the CPT theorem which says that any reasonable quantum field theory must be invariant under the combination of charge reversal (C), parity reversal (P), and time reversal (T). We have known since the 60s that the laws of physics are not invariant under CP reversal (reverse charge and parity); these violations have been experimentally observed, in the physics of Kaons and B-particles. So the CPT theorem implies that any correct physical model must predict the violation of T-symmetry. This symmetry has to be violated in a way that exactly compensates for the violation of the CP symmetry.
Direct violation of T-symmetry has recently been observed by the BaBar experiment.
You seem keen to exclude the thermodynamic arrow of time, but as far as I know that is the only source of time asymmetry.
As Ross mentioned in his answer, the collapse of the wavefunction has been presented as a time asymmetric process. However I would guess most people now view even this as fundamentally time symmetric. If you believe in decoherence the wavefunction collapse is just another example of the thermodynamic arrow of time.
There remains the (basically philosophical) problem of why humans experience time to flow in a single direction, but this too may simply be because the thought process inevitably follows the thermodynamic arrow of time.
There are books on this subject. All the answers I have seen focus on one of two things: the thermodynamic arrow or the quantum collapse. I have not seen any good answer for translating quantum collapse into the large scale world. The thermodynamic argument is quite subtle if you dig into it. From any point in time that entropy is not a maximum, entropy (with huge probability) should increase in both directions.