What would result in a transformer that has its secondary wires disconnected from any circuit?

I am studying magnetism and I am curious as to what happens in a transformer that has its secondary output wires connected through a circuit versus one that doesn't.

My main questions (in the case of the unconnected secondary) are:

Is there more or less resistance on the primary?

Are there equations that describe the heat losses (of the primary and secondary) in this scenario?

Here is from wikipedia a schematic of a transformer:

If V_S is open no current will flow through the secondary circuit. The primary circuit will have the current appropriate to the resistance and impedance of the simple, now, circuit.

This happens all the time when we have a transformer just sitting there, without anything plugged in at the secondary circuit. The transformer draws energy and gets heated up anyway. That is why we are instructed to disconnect unused electrical appliances, and not just switch them off.

Note: the ratios in the schema should be inverted to avoid spurious infinities due to the zero current in V_s

A disconnected secondary, obviously, doesn't send any current through anything. Charge will only slosh back and forth, making the loose wire ends alternate between + and - voltages, with the two ends opposite.

Currents are in a ratio inverse to the number of turns. Whatever that ratio, with no current at all in the seconary, there should be almost no current in the primary. In textbooks, it would be exactly zero, but in the real world we have imperfect materials, so a tiny current may be measurable. I'm not finding a good site or book reference at the moment, but start searching "loss tangent", "dielectric loss", "hysteresis loss" for ways to quantify, estimate and measure the power lost. The effects that depend on magnetic fields will be less important than those depending on electric fields, since there will be little current flowing.

Some hefty voltage applied to the primary, and near zero current, make for huge impedance.

Also keep in mind that, not minding quantum mechanics, any physical system with changing voltages and currents will radiate EM waves, perhaps not very efficiently. To estimate the power lost would require a geometric description of the system suitable for a multipole expansion. There are formulas for that.