Joint ICTP/SISSA Statistical Physics seminar: "Optimal protocols and optimal transport in the physics of small systems"
Starts 29 Nov 2011 11:00
Ends 29 Nov 2011 20:00
Central European Time
SISSA, Santorio Bldg., room 128 1st floor
Small systems in thermal environments such as particles in optical traps or molecular motors can be driven from one state to another while dissipating work. The statistics of work is related to the free energy difference between the states by Jarzynski's relation, but most characteristics of the process e.g. the sample variance of Jarzynski's relation, or expected released heat or expected work itself depend on protocol details. We show that in a Langevin equation setting the optimal protocol is essentially given by the backwards-forwards solution of optimal control, investigated long ago by F. Guerra and L. Morato in the context of stochastic quantization. For the specific case of optimising heat or work the situation simplifies dramatically, and the coupled backwards-forwards solution reduces to only Burgers equation for an auxiliary field, and mass transport by the Burgers velocity field [1].
I will discuss these results and possible extensions and applications. For instance, if temperature is not constant and time and space an analogous simplification occurs but not for the heat but instead for the entropy production in the environment. This is joint work with Paolo-Muratore-Ginanneschi, Carlos Mejia-Monasteiro, Stefano Bo, Antonio Celani and Ralf Eichhorn.
[1] Erik Aurell, Carlos Mejia-Monasterio, Paolo Muratore-Ginanneschi; Optimal protocols and optimal transport in stochastic thermodynamics; Phys. Rev. Lett. 106, 250601 (2011)