# Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state

## Abstract

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for understanding irreversibility and the second law in fundamental chemical and biological processes that are actively driven, thus operating far from thermal equilibrium. Here, we apply the framework of fluctuation theorems to investigate the important case of a system relaxing from a non-equilibrium state towards equilibrium. Using a vacuum-trapped nanoparticle, we demonstrate experimentally the validity of a fluctuation theorem for the relative entropy change occurring during relaxation from a non-equilibrium steady state. The platform established here allows non-equilibrium fluctuation theorems to be studied experimentally for arbitrary steady states and can be extended to investigate quantum fluctuation theorems as well as systems that do not obey detailed balance.

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## Acknowledgements

This research was supported by ETH Zürich, ERC-QMES (no. 338763), ERC-Plasmolight (no. 259196), Fundació Privada CELLEX and the Austrian Science Fund (FWF) within the SFB ViCoM (grant F41). The authors acknowledge support from the ESF Network Exploring the Physics of Small Devices.

## Author information

Authors

### Contributions

L.N. and J.G. conceived and designed the experiments. J.G. performed the experiments. J.G., C.D. and L.N. analysed the data. C.D. developed the theoretical framework. R.Q. contributed materials/analysis tools. J.G., C.D. and L.N. co-wrote the paper.

### Corresponding authors

Correspondence to Christoph Dellago or Lukas Novotny.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary Information (PDF 1002 kb)

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Gieseler, J., Quidant, R., Dellago, C. et al. Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state. Nature Nanotech 9, 358–364 (2014). https://doi.org/10.1038/nnano.2014.40

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