Dissipation in small systems: A Landau-Zener approach

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.

4 pages, 4 figures

References in corpus (4)

• Dissipation: The phase-space perspective
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Exact fluctuation theorem without ensemble quantities
• Landau-Zener transitions mediated by an environment: population transfer and energy dissipation

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• Kinetics and thermodynamics of a driven open quantum system
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• Coherent Long-Range Thermoelectrics in Nonadiabatic Driven Quantum Systems
• Quantum Hamiltonian daemons: unitary analogs of combustion engines