Effective Gibbs state for averaged observables

TL;DR

This paper develops a perturbative approach to derive an effective Hamiltonian for averaged observables, highlighting similarities with the mean force Hamiltonian and discussing thermodynamic implications of measurement limitations.

Contribution

It introduces a perturbative method to compute the effective Hamiltonian for averaged observables and explores its relation to the mean force Hamiltonian and thermodynamics.

Findings

Effective Hamiltonian closely resembles the mean force Hamiltonian.

Measurement restrictions lead to information loss with thermodynamic consequences.

Perturbative calculations provide insights into the structure of the effective Gibbs state.

Abstract

We consider the effective Gibbs state for averaged observables. In particular, we perturbatively calculate the correspondent effective Hamiltonian. We show that there are a lot of similarities between this effective Hamiltonian and the mean force Hamiltonian. We also discuss a thermodynamic role of the information loss due to restriction of our measurement capabilities to such averaged observables.