# Many-body perturbation theory and fluctuation relations for interacting population dynamics

## TL;DR

This paper develops a perturbative theoretical framework for interacting population dynamics, incorporating interactions between organisms, and derives fluctuation relations and variational principles to better understand collective phenomena.

## Contribution

It introduces a novel interacting model for population dynamics and establishes fluctuation relations and variational principles within this framework.

## Key findings

- Derived fluctuation relations for interacting populations
- Established a variational principle for the models
- Provided a perturbative theory applicable to collective phenomena

## Abstract

Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments. However, it is quite difficult to insist on a general statement on living organisms since mathematical models heavily depend on phenomena that we focus on. Recently it was reported that the fluctuation relations on the fitness of living organisms held for a quite general problem setting. But, interactions between organisms were not incorporated in the problem setting, though interaction plays critical roles in collective phenomena in physics and population dynamics. In this paper, we propose interacting models for population dynamics and provide the perturbative theory of population dynamics. Then, we derive the variational principle and fluctuation relations for interacting population dynamics.