Speaker
Prof.
Antonio Celani
(CNRS - Institut Pasteur)
Description
Particle motion at the micro-scale is an incessant
tug-of-war between thermal fluctuations and applied forces
on one side, and the strong resistance exerted by fluid
viscosity on the other. Friction is so strong that
completely neglecting inertia – the overdamped approximation
– gives an excellent effective description of the actual
particle mechanics. In sharp contrast with this result, here
we show that the overdamped approximation dramatically fails
when thermodynamic quantities such as the entropy production
in the environment is considered, in presence of temperature
gradients. In the limit of vanishingly small, yet finite
inertia, we find that the entropy production features a
contribution that is anomalous, i.e. has no counterpart in
the overdamped approximation. This phenomenon, that we call
entropic anomaly, is due to a symmetry-breaking that occurs
when moving to the small, finite inertia limit.
As a consequence of this phenomenon, quasi-static engines,
whose efficiency is maximal in a fluid at uniform
temperature, have in fact vanishing efficiency in presence
of temperature gradients. For slow cycles the efficiency
falls off as the inverse of the period. The maximum
efficiency is reached at a finite value of the cycle period
that is inversely proportional to the square root of the
gradient intensity. The relative loss in maximal efficiency
with respect to the thermally homogeneous case grows as the
square root of the gradient. As an illustration of these
general results, we construct an explicit, analytically
solvable example of a Carnot stochastic engine. In this
thought experiment, a Brownian particle is confined by a
harmonic trap and immersed in a fluid with a linear
temperature profile. This example may serve as a template
for the design of real experiments in which the effect of
the entropic anomaly can be measured.
Antonio Celani, Stefano Bo, Ralf Eichhorn, and Erik Aurell,
Phys. Rev. Lett. 109, 260603 (2012)
Stefano Bo and Antonio Celani, arXiv:1212.1608
