BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ugur Cetiner (Harvard Medical School) DTSTART:20221027T153000Z DTEND:20221027T160000Z DTSTAMP:20260421T124524Z UID:MoRN/56 DESCRIPTION:Title: Re formulating non-equilibrium steady-states\nby Ugur Cetiner (Harvard Me dical School) as part of Seminar on the Mathematics of Reaction Networks\n \n\nAbstract\nMarkov processes are widely used to model stochastic systems in physics and biology. Their steady-state probabilities are given in ter ms of their transition rates by the Matrix-Tree theorem (MTT). The MTT use s spanning trees in a graph-theoretic representation and reveals that\, aw ay from thermodynamic equilibrium\, steady-state probabilities become glob ally dependent on all transition rates and the resulting expressions grow super-exponentially in the graph size. The overwhelming complexity and lac k of thermodynamic insight have impeded analysis\, despite substantial pro gress in proving exact fluctuation theorems away from equilibrium. We expl oit a graph-theoretic representation of Markov processes to reformulate no n-equilibrium steady state probabilities in a way that makes their descrip tions independent of system size and gives them thermodynamic meaning. Our results suggest how we can “follow the energy” to unravel the functio nal logic of non-equilibrium systems in physics and biology.\n LOCATION:https://researchseminars.org/talk/MoRN/56/ END:VEVENT END:VCALENDAR