Steepest Entropy Ascent for Two-State Systems with Slowly Varying Hamiltonians

TL;DR

This paper applies the Steepest Entropy Ascent principle to two-state quantum systems with slowly varying Hamiltonians, demonstrating robustness to thermalization and exploring specific examples like spins in rotating fields.

Contribution

It extends the Steepest Entropy Ascent approach to time-dependent Hamiltonians and analyzes its implications for two-state systems under adiabatic conditions.

Findings

Maximum entropy production principle applies to time-dependent Hamiltonians.

Systems show robustness to thermalization under adiabatic approximation.

Examples include spin in rotating field and avoided crossing scenarios.

Abstract

The Steepest Entropy Ascent approach is considered and applied to few-state systems. When the Hamiltonian of the system is time dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact are given. In the limit of slowly varying Hamiltonians which allows for the adiabatic approximation for the unitary part of the dynamics, the system exhibits significant robustness to the thermalization process. Specific examples such as a spin in a rotating field and a generic two-state system undergoing an avoided crossing are considered.