We develop a field-theoretic framework for work statistics in
O(N) models driven through criticality. By analyzing the dynamic renormalization group flow of composite power operators, we find the Kibble-Zurek scaling laws as a natural consequence of the flow, and we derive the scaling of work cumulants relevant to Kibble-Zurek scaling of topological defects from first principles, bypassing heuristic freeze-out argument. This yields the universal scaling
cn∼τQ−αn for the
n-th work cumulant density: isolated quantum systems exhibit a scaling of
αn=p(d+nz)ν/(1+pzν), whereas open quantum and classical systems undergo a dimensional collapse to
αn=pdν/(1+pzν). Validated by exact Gaussian solutions and numerical simulations, our theory establishes a foundation for general work statistics far from equilibrium, thereby bridging stochastic thermodynamics and the renormalization group theory.
There has been much recent progress on exotic surface critical behavior, yet the classical-quantum correspondence of special and extraordinary-log criticality remains largely unclear. Employing worm Monte Carlo simulations, we explore the surface criticality at an emergent superfluid-Mott insulator critical point in the Villain representation, which is believed to connect classical and quantum O(2) critical systems. We observe a special transition with the thermal and magnetic renormalization exponents
yt=0.58(1) and
yh=1.690(1), respectively, which are close to recent estimates from models with discrete spin variables. The existence of extraordinary-log universality is evidenced by the critical exponent $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}=0.58(2)$ from two-point correlation and the renormalization-group parameter $\ensuremath{\alpha}=0.28(1)$ from superfluid stiffness, which obey the scaling relation of extraordinary-log critical theory and recover the logarithmic finite-size scaling of critical superfluid stiffness in open-edge quantum Bose-Hubbard model. Our results bridge recent observations of surface critical behavior in the classical statistical mechanical models [Parisen Toldin, Phys. Rev. Lett. 126, 135701 (2021); Hu et al., Phys. Rev. Lett. 127, 120603 (2021); Parisen Toldin et al., Phys. Rev. Lett. 128, 215701 (2022)] and the open-edge quantum Bose-Hubbard model [Sun
et al., arXiv:2205.00878 (2022)].
The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way. Among the most striking features of the entanglement entropy are its unbounded linear growth in the thermodynamic limit, its asymptotic extensivity in finite-size systems, and the possibility of measurement-induced phase transitions, all of which have no obvious classical counterpart. Here, we show how these key qualitative features emerge naturally also in classical information spreading, as long as one treats the classical many-body problem on par with the quantum one, that is, by explicitly accounting for the exponentially large classical probability distribution. Our analysis is supported by extensive numerics on prototypical cellular automata and Hamiltonian systems, for which we focus on the classical mutual information and also introduce a ``classical entanglement entropy.'' Our study sheds light on the nature of information spreading in classical and quantum systems, and opens avenues for quantum-inspired classical approaches across physics, information theory, and statistics.