AIMR Math Group Seminar #5



Date : April 27th (Fri.) 10:00~12:00

Place:3C, AIMR Main Bldg., Katahira campus, Tohoku University

SpeakerDr. Andreas Dechant

Title: Currents, fluctuations and entropy in non-equilibrium Markov dynamics



The presence of currents is one of the defining features of out-of-equilibrium systems. For small systems in particular, these currents are generally fluctuating quantities due to the presence of noise. In this talk, I will show that such fluctuating currents in Markovian stochastic dynamics possess some surprising universal properties.
I will give a brief introduction on Markovian dynamics, stochastic currents and the path-integral formulation of stochastic processes. I will discuss how transformations of the dynamics can be used to obtain a bound on the cumulant generating function of the current. This bound can be used to derive an inequality between the response of the current to a small perturbation and the fluctuations of the current. The perturbation can correspond to a physical perturbation of the system – yielding a relation between mobility and diffusivity for steady state particle transport. By considering more general perturbations, I show that a recently derived thermodynamic uncertainty relation can in fact be understood in terms of a symmetry of the system under a rescaling of time.





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