Non-Markovian Dynamics Impact on the Foundations of Statistical Mechanics

TL;DR

This paper investigates how non-Markovian quantum dynamics influence the emergence of thermal equilibrium in statistical mechanics, revealing complex steady states that challenge traditional assumptions.

Contribution

It demonstrates that non-Markovian effects can lead to steady states that preserve initial quantum information, extending the understanding of quantum decoherence beyond classical thermalization.

Findings

Decoherence can result in four different steady states.

Thermal and thermal-like states confirm relaxation to equilibrium.

Quantum memory states maintain initial information, defying classical expectations.

Abstract

The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on non-Markovian dynamics [Phys. Rev. Lett. 109, 170402 (2012)], we find that decoherence of quantum states manifests unexpected complexities. Indeed, an arbitrary given initial quantum state, under the influence of different reservoirs, can evolve into four different steady states: thermal, thermal-like, quantum memory and oscillating quantum memory states. The first two steady states \textit{de facto} provided a rigorous proof how the system relaxes to thermal equilibrium with its environment. The latter two steady states, with strong non-Markovian effects, will maintain the initial state information and not reach thermal equilibrium, which is beyond the conventional wisdom of statistical mechanics.