Internal Seminar: Mapping of uncertainty relations between continuous and discrete time

Internal Seminar: Davide Chiuchiu, Postdoctoral Researcher, Biological Complexity Unit (Simone Pigolotti)

Title : Mapping of uncertainty relations between continuous and discrete time.

Abstract : Currents may qualify among the most important observables to study in a system. Just to name a few examples, quantities like heat, work, entropy production, number of cycles, electrical flows, and mass flows can all be expressed as currents. In macroscopic systems, currents are characterized by their average value. However, the behavior of a given current may drastically change when fluctuations becomes a dominant mechanism in the system. The need to characterize the fluctuating behavior of currents in stochastic systems led, in the recent years, to the discovery of uncertainty relations. Such relations state that the entropy rate-of-change in a system sets a minimum amount of fluctuations on every possible current. Uncertainty relations were believed to be general and independent of the system characteristics. However, it was recently discovered that such lower bounds depend on the nature of time: discrete or continuous. To understand the physical reason, we compare here current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that the random timing of transitions in the master equations makes current fluctuations always more likely. From this analysis we derive a rule to map the moments of a current between discrete and continuous time. We then exploit this mapping to obtain new uncertainty bounds. Our findings show that the quests for uncertainty bounds in discrete and continuous time reduce to a single problem.

Refreshments will be served afterwards. We hope to see you there!

Sincerely,

Internal Seminar Organizing Committee:

Marylka Yoe Uusisaari

Yasha Neiman

Rob Campbell

Margaret Mars Brisbin

​ Maéva Techer

Jigyasa Arora

Yuka Suzuki

Andreas Thomasen

Kung-Lung Li