A topic of discussion in magnetic field analysis is the modeling of magnetic objects using the finite element method. Although a magnetic object located in a weak magnetic field can in some cases be assumed to have a fixed magnetic permeability, it typically varies with the magnetic field’s magnitude, and the magnetic field’s orientation and magnetic flux density also vary. Considering the relationship among vector quantities such as the magnetic field and magnetic flux density as well as the influence of the object’s history, i.e., hysteresis, makes analysis difficult. However, a magnetic object treated as a thermodynamic object can be described by the state quantities of internal energy and free energy, which are scalar. In this case, the magnetic field and magnetic flux density are state variables, and the relationship between the magnetic field and magnetic flux density can be obtained from the free energy if it is handled as a function of magnetic flux density. Consequently, the relationship between these vector quantities can be expressed in terms of a scalar quantity, free energy. Additionally, the laws of thermodynamics require that the thermodynamic potential (a function of the magnetic field and temperature) reach a minimum when the system is in thermal equilibrium, making it possible to use the variational finite element method. Expressing hysteresis with the conventional finite element method that employs the method of weighted residuals is difficult, because it requires handling the magnetic field as a function of magnetic flux density. To address this, this section proposes a method employing variational calculus that handles free energy as a function of magnetic flux density. As a result, the magnetic flux density is not restricted to a single solution for a fixed magnetic field, allowing spontaneous magnetization to be expressed. Further, this method makes it possible to treat the hysteresis of magnetic objects as a physical phenomenon akin to friction. Introducing the concept that the hysteresis of magnetic field is analogous to frictional force makes it possible to model magnetic behavior inclusive of hysteresis.