# Thermodynamics of a Periodically Driven Qubit

## TL;DR

This paper presents a novel approach to analyze the thermodynamics of a periodically driven qubit by embedding its dynamics into an infinite-dimensional system called the dressed-qubit, simplifying the thermodynamic formulation.

## Contribution

It introduces a new method using Floquet theory to embed the qubit dynamics into an infinite-dimensional system, facilitating thermodynamic analysis with ladder operators.

## Key findings

- Successfully derives the stochastic Schrödinger equation for the dressed-qubit.
- Simplifies thermodynamic formulation using ladder operators.
- Recovers known thermodynamic results for the driven qubit.

## Abstract

We aim to give a pedagogic presentation of the open system dynamics of a periodically driven qubit in contact with a temperature bath. We are specifically interested in the thermodynamics of the qubit. It is well known that by combining the Markovian approximation with Floquet theory it is possible to derive a stochastic Schr\"odinger equation in $\mathbb{C}^2$ for the state of the qubit. We follow here a different approach. We use Floquet theory to embed the time-non autonomous qubit dynamics into time-autonomous yet infinite dimensional dynamics. We refer to the resulting infinite dimensional system as the dressed-qubit. Using the Markovian approximation we derive the stochastic Schr\"odinger equation for the dressed-qubit. The advantage of our approach is that the jump operators are ladder operators of the Hamiltonian. This simplifies the formulation of the thermodynamics. We use the thermodynamics of the infinite dimensional system to recover the thermodynamical description for the driven qubit. We compare our results with the existing literature and recover the known results.