This question is quite interesting, and the answer depends on what potential you are asking.
1. I'll start with an answer that you probably didn't ask: any battery (a chemical source of electrical energy) when it drives a circuit discharges with time, so the potential difference between battery terminals does not remain constant but decreases.
2. And perhaps this is what you wanted to ask: when elements such as resistors, capacitors and inductances are connected in parallel to the voltage source (battery or a socket), the potential difference on them is the same, i.e. it is equal to the voltage of the voltage source. But this voltage will decrease with time if they are fed from battery. So in parallel combination potential difference is equal on all elements but it is not necessarily constant.
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