What are the actions of an electrical circuit if the circuit is found open?

Electrons cannot traverse or move thru an open circuit. Therefore there is no current or 'electron' flow. Voltage may be present with an open circuit but it is doing no 'work'.

Compare an open circuit with 'potential' energy. Even though potential energy exist there is no kinetic energy unless the electrons have a path to take.

An open circuit provides no such path.

Kinetic energy means something with mass is moving and in some cases that movement is harnessed to accomplish 'work'.

Potential (voltage) which is doing nothing because a circuit is open cannot accomplish any work since there are no electrons moving.

Another perspective:

If an electric circuit is opened, the electricity flow stops. This is due to the fact that air is a strong insulator, and most amounts of electricity (save for lightning) do not have enough voltage to overcome this resistance (in a process called ionization). This is reflected in a formula V = I × R where r is resistance, i is amperage, and v is voltage. Through this relationship, as resistance reaches a high level, voltage drops, and the electric flow stops because it cannot overcome the resistance with the force of voltage or amps.

A thought on the ionization process:

As ionization occurs, resistance across the 'gap path' drops and voltage, if not regulated will drop as well. When there is not enough voltage to cause ionization the voltage will be higher than at the time ionization occurs.

At ionization, current (I) will increase, resistance (R) will decrease and voltage (E) will decrease as well and the potential (voltage) is now causing energy or electrons to flow.

As the ionization occurs much less voltage or potential is required to maintain the ionization path than is required to achieve ionization to start with.

Example: A cars ignition coil is capable of producing 45K~50K volts of electricity.

Yet when the voltage is measure at the end of the spark plug wire there will be only 9K or 10K volts due to the air/fuel molecules being ionized

Not to sure ionization actually is applicable to the original question however. :0)

BTW, I'm 'old school' where E=I x R where E = Voltage.

Just like megacycles to megahertz, I guess everything changes but the laws of physics.