We develop an exact finite-perturbation response theory for the higher-order statistics of general state observables in nonequilibrium Markov networks. For local perturbations, the moment generating function obeys an exact nonlinear response identity in the perturbation strength, controlled by a single kinetic parameter
α
. This induces an exact nonlinear map for the cumulant generating function and closed expressions for finite responses of all cumulants through partial Bell polynomials. As a central application, we obtain a complete theory of variance control, including sharp saturation limits, a classification of monotone-suppression and sign-reversal regimes, and meanfirst-passage-time design principles for optimal noise suppression. The same framework yields exact formulas for operational and symmetrized response resolution along the accessible control branch. A four-state gene-regulation model illustrates how local kinetic control suppresses the occupancy noise of a transcriptionally competent promoter state.
We study simultaneous inference for maxima of canonical order-two $U$-statistics in high dimension. Degeneracy makes quadratic fluctuations leading, so ordinary Gaussian calibration can fail even after exact variance normalization. We show that the appropriate general target is a joint signed Gaussian quadratic chaos a...
Thermodynamic uncertainty relations connect current fluctuations to dissipation and, in certain settings, can emerge from underlying fluctuation-response relations. However, in underdamped dynamics, conventional mean-current uncertainty relations can fail, and the underlying connection between fluctuations, response, a...
Tan Van Vu, Van Tuan Vo, Ruicheng Bao et al.· 1 citation
We study how the spatial profile of a deterministic coherent gate perturbation affects finite-size quasienergy statistics and operator dynamics in U(1)-symmetric XXZ Floquet circuits. Using a shared homogeneous reference, we compare a single modified bond with an alternating perturbation applied across the whole chain....
We develop a spectral theory for dynamical large deviations in non-Markov jump processes and non-Markov chains, whose dynamics depends on the past through state- and jump-dependent empirical observables. We demonstrate that a multiscale Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) Ansatz separates fast configurational rel...
We investigate a discontinuous route from integrability to chaos using a confined stochastic random walk and a deterministic stadium-like billiard. In both systems, the stationary diffusive observable exhibits a finite jump at the transition: it vanishes at the unperturbed limit but approaches a finite, geometry-contro...
A. K. P. da Fonseca, Marcelo de Almeida Presotto, D. M. Oliveira et al.· 0 citations
Jarzynski's equality recovers an equilibrium free-energy difference from nonequilibrium work trajectories, but its exponential average can converge very slowly because rare trajectories carry large weight. We show that coarse thermodynamic information measured at the nonequilibrium endpoint can reduce this sampling bur...
B. Ahmadi· 0 citations
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