# Quantum thermodynamics in adiabatic open systems and its trapped-ion experimental realization

## TL;DR

This paper explores quantum thermodynamics in open systems undergoing adiabatic processes, establishing theoretical conditions for heat and work, and demonstrates an experimental realization using a trapped-ion system to analyze thermodynamic quantities.

## Contribution

It introduces a theoretical framework for adiabatic processes in open quantum systems and demonstrates an experimental realization with trapped ions.

## Key findings

- Defined heat and work in non-unitary quantum evolutions.
- Established conditions for adiabaticity without heat exchange.
- Experimentally measured thermodynamic quantities in a trapped-ion system.

## Abstract

Quantum thermodynamics aims at investigating both the emergence and the limits of the laws of thermodynamics from a quantum mechanical microscopic approach. In this scenario, thermodynamic processes with no heat exchange, namely, adiabatic transformations, can be implemented through quantum evolutions in closed systems, even though the notion of a closed system is always an idealization and approximation. Here, we begin by theoretically discussing thermodynamic adiabatic processes in open quantum systems, which evolve non-unitarily under decoherence due to its interaction with its surrounding environment. From a general approach for adiabatic non-unitary evolution, we establish heat and work in terms of the underlying Liouville superoperator governing the quantum dynamics. As a consequence, we derive the conditions that an adiabatic open-system quantum dynamics implies in the absence of heat exchange, providing a connection between quantum and thermal adiabaticity. Moreover, we determine families of decohering systems exhibiting the same maximal heat exchange, which imply in classes of thermodynamic adiabaticity in open systems. We then approach the problem experimentally using a hyperfine energy-level quantum bit of an Ytterbium $^{171}$Yb$^+$ trapped ion, which provides a work substance for thermodynamic processes, allowing for the analysis of heat and internal energy throughout a controllable engineered dynamics.