Dissipation in small systems: A Landau-Zener approach

TL;DR

This paper develops a stochastic thermodynamics framework for small Fermionic systems driven by time-dependent forces, using Landau-Zener theory to analyze energy exchange, work, heat, and dissipation.

Contribution

It introduces a novel Landau-Zener based approach to model dissipation and thermodynamics in small quantum systems interacting with reservoirs.

Findings

Accurately reproduces quantum work statistics.

Provides explicit dissipation expressions in terms of diabatic transitions.

Establishes a thermodynamics framework for driven Fermionic levels.

Abstract

We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expression for the dissipation in terms of diabatic transitions.