Variational properties of a pumped dynamical system

TL;DR

This paper extends a generalized entropy framework to analyze pumped dynamical systems, demonstrating how populations introduced externally influence system evolution and providing numerical insights into two-level systems with pumping and relaxation.

Contribution

It generalizes the entropy-based approach to include external pumping in dynamical systems, linking it to previous models and demonstrating its physical relevance.

Findings

The formalism applies to pumped systems with decay.

Numerical results show behavior of two-level systems with pumping.

The approach captures monotonic entropy evolution in pumped scenarios.

Abstract

We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial state of the system. In this paper, we generalize the treatment to the case when population is pumped into the system from levels not explicitly considered. These populations then pass through the coupled levels and exit by decay to levels outside the system. We derive the form of the equation of motion and relate it to our earlier treatments. It turns out that the formalism can be generalized to the new situation. Its physically relevant features are demonstrated, and the behaviour obtained is illustrated by numerical treatment of the standard two-level system with pumping and relaxation included.