Martingales and gambling in stochastic thermodynamics

by Prof. Edgar Roldan (ICTP)

Wednesday 22 Dec 2021, 10:00 → 11:00 Europe/Rome

1/1-2 - Aula "C. Voci" (Dipartimento di Fisica e Astronomia - Edificio Marzolo)

Martingales have a central role in the theory of stochastic process and
find important applications in mathematical finance, yet they have been
not much explored in physics.
We have found recently that many fundamental concepts in statistical
physics, such as the non-equilibrium nature of certain processes, can be
naturally associated with martingales. In stochastic thermodynamics, we
have found that this association with martingales often leads to a
drastic simplification and permits to easily derive novel results that
would be very difficult to obtain with other means. This includes
universal equalities and inequalities for the extreme-value and
first-passage time statistics of entropy production  in nonequilibrium
stationary states, which we have tested in various experimental systems.
Very recently, we have extended our theory to nonequilibrium systems
that are subject to time-dependent deterministic protocols. To this aim,
we introduce and realize "demons" that follow a customary gambling
strategy to stop a nonequilibrium process at stochastic times. For these
systems, we find that the average work done until a stopping condition
takes place can exceed the average nonequilibrium free energy change
until the stopping event. We test this result in a single electron box,
identifying  efficient gambling strategies that lead to negative
dissipation.

I Neri, É Roldán, F Jülicher
Phys. Rev. X 7 (1), 011019 (2017)

G Manzano, D Subero, O Maillet, R Fazio, JP Pekola, É Roldán
Phys. Rev. Lett. 126 (8), 080603 (2021)

v2_MartingalesPadova2021.pdf