Reformulating non-equilibrium steady-states

Abstract: Markov processes are widely used to model stochastic systems in physics and biology. Their steady-state probabilities are given in terms of their transition rates by the Matrix-Tree theorem (MTT). The MTT uses spanning trees in a graph-theoretic representation and reveals that, away from thermodynamic equilibrium, steady-state probabilities become globally dependent on all transition rates and the resulting expressions grow super-exponentially in the graph size. The overwhelming complexity and lack of thermodynamic insight have impeded analysis, despite substantial progress in proving exact fluctuation theorems away from equilibrium. We exploit a graph-theoretic representation of Markov processes to reformulate non-equilibrium steady state probabilities in a way that makes their descriptions independent of system size and gives them thermodynamic meaning. Our results suggest how we can “follow the energy” to unravel the functional logic of non-equilibrium systems in physics and biology.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

---

Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom!

The organizers.

---