Faster Uphill Relaxation in Thermodynamically Equidistant Temperature Quenches

Abstract

We uncover an unforeseen asymmetry in relaxation: for a pair of thermodynamically equidistant temperature quenches, one from a lower and the other from a higher temperature, the relaxation at the ambient temperature is faster in the case of the former. We demonstrate this finding on hand of two exactly solvable many-body systems relevant in the context of single-molecule and tracer-particle dynamics. We prove that near stable minima and for all quadratic energy landscapes it is a general phenomenon that also exists in a class of non-Markovian observables probed in single-molecule and particle-tracking experiments. The asymmetry is a general feature of reversible overdamped diffusive systems with smooth singlewell potentials and occurs in multiwell landscapes when quenches disturb predominantly intrawell equilibria. Our findings may be relevant for the optimization of stochastic heat engines.

Anomalous heating in a colloidal system

“…In the Kovacs effect, protocols that drive the system out of equilibrium can produce nonmonotonic relaxations that show crossings in a quantity that monitors distance from equilibrium ( 7 , 52 – 55 ). It may also be interesting to apply the feedback trap techniques used here to test experimentally the recent prediction that warming can be generically faster than cooling, for equal positive and negative free-energy deviations from thermodynamic equilibrium ( 27 , 56 , 57 ). The concepts of anomalous relaxation that we explore here for the inverse Mpemba effect may lead to a unified picture where all these effects can be seen as representatives of a broad class of physical phenomena.…”

“…From this point of view, the dynamics of cooling and heating obey similar principles, and anomalous heating represents an inverse Mpemba effect. Yet, despite a formal similarity between the cases of heating and cooling ( 1 , 27 ), anomalous heating has not previously been seen experimentally, neither in systems that exhibited the anomalous cooling effect ( 10 – 16 , 26 , 28 – 30 ) nor in any other system.…”

Estimating time-dependent entropy production from non-equilibrium trajectories

“…It will also be interesting to test whether these results can be used to infer new information from existing empirical data from molecular motors such as kinesin 71 or F 1 -ATPase 72,73 . The thermodynamics of cooling or warming up in classical systems 74 or the study of quantum systems being monitored by a sequence of measurements [75][76][77][78] are other promising areas to which these results can be applied. 19)), and (g)(h) with the synchronization error (Eq.…”

Optimal Control of Uniformly Heated Granular Fluids in Linear Response

“…This kind of time optimisation problem is important from a fundamental point of view and also has relevance for applications. For the connection between equilibrium states, related problems emerge in the optimisation of irreversible heat engines [ 46 ], the analysis of the Mpemba effect [ 21 , 47 , 48 , 49 ], and the optimisation of the relaxation route to equilibrium [ 50 , 51 , 52 ].…”