Energy conversion theorems for some linear steady-states

One of the main issues that real energy converters present, when they produce effective work, is the inevitable entropy production. Within the context of Non-equilibrium Thermodynamics, entropy production tends to energetically degrade man-made or living systems. On the other hand, it is also not useful to think about designing an energy converter that works in the so-called minimum entropy production regime since the effective power output and efficiency are zero. In this manuscript, we establish some \textit{Energy Conversion Theorems} similar to Prigogine's one with constrained forces, their purpose is to reveal trade-offs between design and the so-called operation modes for $\left(2\times2\right)$--linear isothermal energy converters. The objective functions that give rise to those thermodynamic constraints show stability. A two--meshes electric circuit was built as an example to demonstrate the Theorems' validity. Likewise, we reveal a type of energetic hierarchy for power output, efficiency and dissipation function when the circuit is tuned to any of the operating regimes studied here: maximum power output ($MPO$), maximum efficient power ($MP\eta$), maximum omega function ($M\Omega$), maximum ecological function ($MEF$), maximum efficiency ($M\eta$) and minimum dissipation function ($mdf$).