Does a moving particle count as a wave?

[renormalize]

"Equilibrium is essentially the baseline we choose for a given physical system." If you disagree with this statement, I would appreciate it if you could provide a more rigorous alternative definition of equilibrium.

This is a more rigorous (https://www.britannica.com/science/equilibrium-physics):
equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely. For a single particle, equilibrium arises if the vector sum of all forces acting upon the particle is zero. A rigid body (by definition distinguished from a particle in having the property of extension) is considered to be in equilibrium if, in addition to the states listed for the particle above, the vector sum of all torques acting on the body equals zero so that its state of rotational motion remains constant. An equilibrium is said to be stable if small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body or particle to the equilibrium state. Examples include a weight suspended by a spring or a brick lying on a level surface. An equilibrium is unstable if the least departure produces forces that tend to increase the displacement. An example is a ball bearing balanced on the edge of a razor blade.

 

[far far away]

This is a more rigorous (https://www.britannica.com/science/equilibrium-physics):
equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely. For a single particle, equilibrium arises if the vector sum of all forces acting upon the particle is zero. A rigid body (by definition distinguished from a particle in having the property of extension) is considered to be in equilibrium if, in addition to the states listed for the particle above, the vector sum of all torques acting on the body equals zero so that its state of rotational motion remains constant. An equilibrium is said to be stable if small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body or particle to the equilibrium state. Examples include a weight suspended by a spring or a brick lying on a level surface. An equilibrium is unstable if the least departure produces forces that tend to increase the displacement. An example is a ball bearing balanced on the edge of a razor blade.

Thank you, but the resource you shared reads more like an extended introduction or overview of the concept of equilibrium rather than a single, compact definition.