Brownian Thermometry Beyond Equilibrium

TL;DR

This paper reviews recent advances in Brownian thermometry beyond equilibrium, focusing on heterogeneous temperature fields, effective temperatures, and applications in active and biological matter, with experimental validation.

Contribution

It provides a comprehensive overview of generalized Brownian thermometry techniques, including effective temperature concepts and their practical applications in non-equilibrium systems.

Findings

Effective temperatures can be explicitly computed and experimentally confirmed in non-equilibrium conditions.

Brownian thermometry can be extended to spatially heterogeneous and active systems.

Measurement of temperature spectra via Brownian thermospectrometry enhances understanding of non-thermal environments.

Abstract

Since Albert Einstein's seminal 1905-paper on Brownian motion, the temperature of fluids and gases of known viscosity can be deduced from observations of the fluctuations of small suspended probe particles. We summarize recent generalizations of this standard technique of Brownian thermometry to situations involving spatially heterogeneous temperature fields and other non-equilibrium conditions in the solvent medium. The notion of effective temperatures is reviewed and its scope critically assessed. Our emphasis is on practically relevant real-world applications, for which effective temperatures have been explicitly computed and experimentally confirmed. We also elucidate the relation to the more general concept of (effective) temperature spectra and their measurement by Brownian thermospectrometry. Finally, we highlight the conceptual importance of non-equilibrium thermometry for active and biological matter, such as microswimmer suspensions or biological cells, which often play the role of non-thermal ('active') heat baths for embedded Brownian degrees of freedom.