A trajectory-level derivation shows mutual linearity holds for non-stationary Markov jump processes and generalizes to other systems.
Maes, Response theory: a trajectory-based approach, Frontiers in Physics8, 229 (2020)
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Derives nonlinear response relations for Markovian stochastic systems as covariances with a Bell-polynomial conjugate variable set by stochastic entropy production, plus associated fluctuation-response inequalities.
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Mutual Linearity in and out of Stationarity for Markov Jump Processes: A Trajectory-Based Approach
A trajectory-level derivation shows mutual linearity holds for non-stationary Markov jump processes and generalizes to other systems.
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Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
Derives nonlinear response relations for Markovian stochastic systems as covariances with a Bell-polynomial conjugate variable set by stochastic entropy production, plus associated fluctuation-response inequalities.