  The inverse problem treated in this article consists in reconstructing the
electrical conductivity from the free response of the system in the
magneto-quasi-stationary (MQS) limit. The MQS limit corresponds to a diffusion
PDE. In this framework, a key role is played by the Monotonicity Principle,
that is a monotone relation connecting the unknown material property to the
(measured) free-response. MP is relevant as basis of noniterative and real-time
imaging methods.
  Monotonicity Principles have been found in many different physical problems
governed by PDEs of different nature. Despite its rather general nature, each
different physical/mathematical context requires to discover the proper
operator showing MP. For doing this, it is necessary to develop ad-hoc
mathematical approaches tailored on the specific framework.
  In this article, we prove a monotonic relationship between the electrical
resistivity and the time constants characterizing the free-response for MQS
systems. The key result is the representation of the induced current density
through a modal representation. The main result is based on the analysis of an
elliptic eigenvalue problem, obtained from separation of variables.
