# Bath energy for correlated initial states versus information flow in local dephasing channels

## TL;DR

This paper investigates how initial correlations and spectral density properties influence energy exchange and information flow in local dephasing channels, revealing that initial conditions significantly affect long-term energy and information dynamics.

## Contribution

It introduces a detailed analysis of bath energy variations under correlated initial states and their relation to information flow, highlighting the impact of spectral density features.

## Key findings

- Bath and correlation energy vary monotonically over time depending on the ohmicity parameter.
- Initial correlations can transfer information flow characteristics to energy dynamics.
- Spectral density low-frequency structures determine the direction of energy and information exchange.

## Abstract

Variations of the bath energy are compared with the information flow in local dephasing channels. Special correlated initial conditions are prepared from the thermal equilibrium of the whole system, by performing a selective measurement on the qubit. The spectral densities under study are ohmic-like at low frequencies and include logarithmic perturbations of the power-law profiles. The bath and the correlation energy alternately increase or decrease, monotonically, over long times, according to the value of the ohmicity parameter, following logarithmic and power laws. Consider initial conditions such that the environment is in a thermal state, factorized from the state of the qubit. In the super-ohmic regime the long-time features of the information flow are transferred to the bath and correlation energy, by changing the initial condition from the factorized to the specially correlated, even with different temperatures. In fact, the low-frequency structures of the spectral density that provide information backflow with the factorized initial condition, induce increasing (decreasing) bath (correlation) energy with the specially correlated initial configuration. By performing the same change of initial conditions, the spectral properties providing information loss, produce decrease (increase) of the bath (correlation) energy.