Skewness and kurtosis in stochastic thermodynamics

The thermodynamic uncertainty relation is a prominent result in stochastic thermodynamics that provides bound on the fluctuations of any flux, also known as current, terms average rate entropy production. Such are quantified by second moment probability distribution current. role higher order standardized moments such skewness and kurtosis remains largely unexplored. We analyze associated with first passage time currents within framework thermodynamics. develop method to evaluate For systems unicyclic network states, we conjecture upper lower bounds These depend number states force drives system out equilibrium. show these for do not hold multicyclic networks. discuss application our results infer an underlying states.