Mathematical Physics Seminar (May 29th) – Dr Sarah Loos (Cambridge) – Thermodynamics and optimal control of small-scale processes with memory

Abstract: A central assumption in stochastic thermodynamics is Markovianity, i.e. that one can single out a finite number of mesoscopic degrees of freedom coupled to a heat bath with no internal structure that remains in equilibrium at all times. However, realistic environments has timescales comparable to those of the process under study, leading to memory effects and a temporarily non-equilibrium bath. This is the case, for example, with subcellular transport processes that typically take place in viscoelastic media.
To go beyond this paradigm, we consider thermodynamic properties of systems described by generalized Langevin equations. We consider the canonical control problem of moving a harmonic trap containing a Brownian particle over a given distance in a given time with minimum work input. For viscous media, it is known that the optimal protocol exhibits sudden jumps at the beginning and at the end and has constant speed in between [1]. We show that memory effects in the environment significantly alter the optimal strategies, so that the dragging speed has to be continuously modulated. Surprisingly, the optimal solutions possess a universal time-reversal symmetry for all linear media, independent of the properties of the memory kernel and coloured noise; i.e., also for glassy, granular, and active media. We present experimental evidence for our findings using a colloidal particle dragged by an optimal trap through viscous and viscoelastic fluids [2].
To resolve the spatio-temporal correlations in the environment, we further explore a type of modelling where we combine a Langevin equation for the particle with a scalar fluctuating field theory for the medium [3].

[1] T. Schmiedl and U. Seifert, PRL 98, 108301, (2007).
[2] Loos, Monter, Ginot, and Bechinger, PRX in press (2024).
[3] Venturelli, Loos, Walter, Roldan, and Gambassi, EPL 146, 27001 (2024).

Note: this seminar will be happening in-person only.