Optimal Time-Entropy Bounds and Speed Limits for Brownian Thermal Shortcuts.

By controlling the variance of the radiation pressure exerted on an optically trapped microsphere in real time, we engineer temperature protocols that shortcut thermal relaxation when transferring the microsphere from one thermal equilibrium state to another. We identify the entropic footprint of such accelerated transfers and derive optimal temperature protocols that either minimize the production of entropy for a given transfer duration or accelerate the transfer for a given entropic cost as much as possible. Optimizing the trade-off yields time-entropy bounds that put speed limits on thermalization schemes. We further show how optimization expands the possibilities for accelerating Brownian thermalization down to its fundamental limits. Our approach paves the way for the design of optimized, finite-time thermodynamics for Brownian engines. It also offers a platform for investigating fundamental connections between information geometry and finite-time processes.

Reply to "Comment on 'Harvesting information to control nonequilibrium states of active matter' ".

We stress that the limitations on one of the results of our paper [R. Goerlich et al., Phys. Rev. E 106, 054617 (2022)2470-004510.1103/PhysRevE.106.054617], which are mentioned in the preceding Comment [A. Bérut, preceding Comment, Phys. Rev. E 107, 056601 (2023)10.1103/PhysRevE.107.056601], were actually already acknowledged and discussed in the original publication. Although the observed relationship between the released heat and the spectral entropy of the correlated noise is not universal (but limited to one-parameter Lorentzian spectra), the existence of such a clear relationship is a solid experimental finding. It not only gives a convincing explanation for the surprising thermodynamics observed in the transitions between nonequilibrium steady states, but also provides new tools for the analysis of nontrivial baths. In addition, by using different measures of the correlated noise information content, it may be possible to generalize these results to non-Lorentzian spectra.

Harvesting information to control nonequilibrium states of active matter.

We propose to use a correlated noise bath to drive an optically trapped Brownian particle that mimics active biological matter. Due to the flexibility and precision of our setup, we are able to control the different parameters that drive the stochastic motion of the particle with unprecedented accuracy, thus reaching strongly correlated regimes that are not easily accessible with real active matter. In particular, by using the correlation time (i.e., the "color") of the noise as a control parameter, we can trigger transitions between two nonequilibrium steady states with no expended work, but only a calorific cost. Remarkably, the measured heat production is directly proportional to the spectral entropy of the correlated noise, in a fashion that is reminiscent of Landauer's principle. Our procedure can be viewed as a method for harvesting information from the active fluctuations.