Limits to Energy Conversion

TL;DR

This paper explores fundamental limitations on energy transfer in systems with two power ports, linking thermodynamic principles to system-theoretic properties like cyclo-passivity, and provides conditions for such limitations in port-Hamiltonian systems.

Contribution

It introduces the concept of one-port cyclo-passivity, connecting thermodynamic constraints to system theory, and derives sufficient conditions for this property in port-Hamiltonian systems.

Findings

Identifies conditions under which systems exhibit one-port cyclo-passivity.

Demonstrates the concept across various physical systems.

Establishes fundamental energy transfer limitations based on system properties.

Abstract

A consequence of the Second Law of thermodynamics is that no thermodynamic system with a single heat source at constant temperature can convert heat into mechanical work in a recurrent manner. First we note that this is equivalent to cyclo-passivity at the mechanical port of the thermodynamic system, while the temperature at the thermal port of the system is kept constant. This leads to the general system-theoretic question which systems with two power ports have similar behavior: when is a system cyclo-passive at one of its ports, while the output variable at the other port (such as the temperature in the thermodynamic case) is kept constant? This property is called `one-port cyclo-passivity', and entails, whenever it holds, a fundamental limitation to energy transfer from one port (where the output is kept constant) to the other port. Sufficient conditions for one-port cyclo-passivity are derived for systems formulated in general port-Hamiltonian form. This is illustrated by a variety of examples from different {(multi-)}physical domains; from coupled inductors and capacitor microphones to synchronous machines.