Quarks do not "run around" in the conventional sense like particles in classical physics. Instead, quarks are governed by the laws of quantum mechanics, which describe the behavior of particles at the microscopic level.
In the context of the strong nuclear force, which binds quarks together, quarks are confined within composite particles such as protons and neutrons. This phenomenon is known as confinement. The strong force between quarks becomes stronger as they move apart, making it energetically favorable for quarks to remain bound within these composite particles. As a result, isolated quarks have not been observed in nature.
The energy associated with quarks and their interactions comes from a variety of sources. One important source is the potential energy stored in the strong force field that binds quarks together. This energy is analogous to the potential energy in a stretched spring. The strong force field is generated by the exchange of gluons, which are the carriers of the strong force.
Additionally, in the quantum realm, energy can be spontaneously created and annihilated due to the uncertainty principle. Virtual particles, including virtual quark-antiquark pairs, can be created from the vacuum for very short durations. These virtual particles contribute to the overall energy of the system.
It's worth noting that the concept of energy in quantum field theory is more abstract than in classical physics. Energy is associated with the different quantum fields, including the quark field, and it manifests as various particles and interactions. The exact details of how energy is distributed and exchanged among particles are described by the mathematical framework of quantum field theory.
In summary, quarks do not freely run around, but are confined within composite particles due to the strong nuclear force. The energy associated with quarks and their interactions comes from the potential energy of the strong force field and the dynamics of quantum fields.