Energy conversion theorems for some linear steady-states

TL;DR

This paper establishes energy conversion theorems for linear steady-state energy converters, revealing trade-offs between power, efficiency, and dissipation, supported by a circuit example and analysis of various optimal regimes.

Contribution

It introduces new thermodynamic theorems for linear energy converters, highlighting stability and energetic hierarchies across different operational regimes.

Findings

Theorems reveal trade-offs between power, efficiency, and dissipation.

A circuit example validates the theorems.

Hierarchies among operational regimes are demonstrated.

Abstract

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 ($mdf$).