Brownian Thermometry Beyond Equilibrium

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.

Ultrafast viscosity measurement with ballistic optical tweezers

“…We expect the capability for real-time viscosity measurements developed here to provide new insights into a wide range of out-of-equilbrium systems. Deep questions remain around the connection between microscopic and macroscopic behaviour [10,40], about the existence and applicability of fundamental thermodynamic laws [29], and about the mechanisms for observed behaviours [15,41]. The speed of existing measurements is a key barrier to answering these questions.…”

“…This is predicted to have significant consequences for out-of-equilibrium systems. For example, it causes the effective temperatures of the position and velocity of a hot Brownian particle to diverge [28,29]. Here, we use it to reduce the integration time required for precise viscosity measurements, and therefore to increase the speed of the measurement.…”

Cooperation and competition in the collective drive by motor proteins: mean active force, fluctuations, and self-load

“…Even in a steady state, the generalized fluctuation-response relation involves an additive correction that depends on the steady-state current. [85][86][87][88][89] As we found from numerical simulations, the diffusivity of the filament remains proportional to its mobility at all values of activity. This allows us to use the ratio of long-time diffusivity and mobility, eqn ( 21) and ( 24), to define an effective temperature,…”

Rotation and Revolution of Optically Trapped Gold Nanorods Induced by the Spin and Orbital Angular Momentum of a Laguerre–Gaussian Vortex Beam

“…Rotational and translational temperatures may differ because they describe different degrees of freedom; that is, r t ≠ T T. Moreover, the temperature describing Brownian motion (T t,r in the denominator of Equation (2c,d)) may differ from that describing hydrodynamic Stokes frictions ( t,r η T in Equation (3a,b));, that is, t,r t ,r ≠ η T T . [33]…”