Title: Martingales and gambling in stochastic thermodynamics

Speaker: Édgar Roldán (International Centre for Theoretical Physics)

Abstract:

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.

Event’s info sent to the CSM mailing list.