Martingale theory for stochastic thermodynamics : extrema, stopping times, and gambling

by Dr Édgar Roldán (Abdus Salam International Centre for Theoretical Physics (ICTP))

Thursday 3 Dec 2020, 13:00 → 14:00 Europe/Stockholm

Nordita (Zoom ID: 694 7492 8449)

We describe nonequilibrium fluctuations of entropy production, heat and 
work in classical and quantum mesoscopic systems using the theory of 
Martingales, a mathematical framework widely used in finance.
 

For non-equilibrium steady states, we use martingale theory to study 
the statistics of extrema, stopping times and passage probabilities of 
entropy production, and show that they are universal for Langevin 
processes. In particular, we derive equalities and inequalities for the stopping 
and extreme-value statistics of the entropy production and work, and 
test these results experimentally with an electronic double dot.

We have recently extended our formalism to  Markovian non-stationary 
processes. To this aim, we introduce ''gambling demons'' which stop a 
nonequilibrium process at a finite time using a customary criterion.  
For such demons, the average work done on a small system can be below 
the free energy change, a result which challenges the classical second 
law of thermodynamics. Our work paves the way towards work extraction 
strategies inspired in knowledge in quantitative finance.

[1] I. Neri, E. Roldan, F. Julicher, PRX 7, 011019 (2017)
[2] S. Pigolotti, I. Neri, E. Roldan, F. Julicher, PRL 119(14), 140604 (2017)
[3] R. Chetrite, S. Gupta, I. Neri, E. Roldan, EPL 99, 115422 (2019)
[4] I. Neri, E. Roldan, S. Pigolotti, F. Julicher, J. Stat. Mech. 2019 (10), 104006 (2019)
[5] G. Manzano et. al, arXiv:2008.01630v2 (2020)