Refined Second Law of Thermodynamics for fast random processes

KTH/Nordita/SU seminar in Theoretical Physics [before December 2013]

Wednesday 15 February 2012
from 11:00
to 12:00 at
FB52 (OBS)

Speaker :

Erik Aurell (KTH)

Abstract :

With the advent of micromanipulation it has become possible to pull apart single molecules
with forces in the pN range over distances in the nm range. This means
that one can now control small physical systems, where the control has to compete
with thermal noise. Prime examples are beads in optical traps or molecular motors.
We have studied the problem of minimizing (expected) dissipated work or released heat in such processes.
The problem can be mathematically stated as a standard stochastic optimization problem, but turns out to have
a suprisingly simple solution in turns of Burgers equation (or nonlinear diffusion equation) for an auxiliary field,
and mass transport by the corresponding velocity field [1].
One application of these results is an improvement of Landauer's bound on the heat released when setting one bit
if it has to be done in a finite time [2]. If temperature is not constant in time and/or space an analogous simplification occurs for the entropy production in the environment, but not for released heat.
This is joint work with Paolo-Muratore-Ginanneschi, Carlos Mejia-Monasteiro, Krzysztof Gawedzki, Roya Mohayaee,
Stefano Bo, Antonio Celani and Ralf Eichhorn.

[1] Erik Aurell, Carlos Mejia-Monasterio, Paolo Muratore-Ginanneschi,
Phys. Rev. Lett. 106, 250601 (2011)

[2] Erik Aurell, Krzysztof Gawȩdzki, Carlos Mejía-Monasterio, Roya Mohayaee, Paolo Muratore-Ginanneschi
[arXiv:1201.3207]