Abstract

In this talk, I will introduce occupation uncertainty relations (OURs) for dynamics of Markov processes over discrete configurations. Those are lower bounds on fluctuations rates of system observables that are time integrated along stochastic trajectories. They correspond to a matrix bound on correlations between times spent in different system configurations, i.e., occupation times, which is expressed only in terms of stationary probabilities and lifetimes of individual configurations. It follows that any dynamics that saturates the bound is optimal in approximating stationary distribution by occupation times; I will demonstrate this always occurs for unidirectional cycles. I will also discuss how using this bound, dynamic correlations for a general Markov process can be asymptotically bounded in terms of static correlations, in turn leading to the positivity of dynamic exponents in the thermodynamic limit.