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 single-well potentials and occurs in multiwell landscapes when quenches disturb predominantly intrawell equilibria. Our findings may be relevant for the optimization of stochastic heat engines.
Highlights
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
These pioneering ideas were consistently generalized in numerous ways, most notably, to thermodynamics along individual stochastic trajectories driven far from equilibrium at weak [12,13] and strong [14,15,16,17,18] coupling with the bath, anomalous diffusion phenomena [19,20,21,22], and the so-called “frenesis” focusing on the dynamical activity—a dynamic counterpart to changes in entropy [23,24]
It is possible to probe the transient, nonequilibrium dynamics of colloids and single molecules, e.g., by temperature-modulated particle tracking [4] and timemodulated [44], temperature-modulated [45], temperaturejump [46], and holographic [47] optical tweezers, as well as optical pushing [48]. These experiments allow for systematic investigations of the dependence of relaxation on the direction of the displacement from equilibrium, which is the central question of the present Letter
Summary
Relaxation close to equilibrium was described by the mechanical Onsager-Casimir [9,10] and thermal Kubo-Yokota-Nakajima [11] linear laws These pioneering ideas were consistently generalized in numerous ways, most notably, to thermodynamics along individual stochastic trajectories driven far from equilibrium at weak [12,13] and strong [14,15,16,17,18] coupling with the bath, anomalous diffusion phenomena [19,20,21,22], and the so-called “frenesis” focusing on the dynamical activity—a dynamic counterpart to changes in entropy [23,24]. The blue and red points depict a pair of thermodynamically equidistant temperature quenches, T − and Tþ, with corresponding excess potential energies hΔUiT Æ ≡ hUð0þÞiT Æ − hUi1
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