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.
This paper compares theory and experiment for behavior very near critical points. The primary experimental results are the "critical indices" which describe singularities in various thermodynamic derivatives and correlation functions. These indices are tabulated and compared with theory. The basic theoretical ideas are introduced via the molecular field approach, which brings in the concept of an order parameter and suggests that there are close relations among different phase transition problems. Although this theory is qualitatively correct it is quantitatively wrong, it predicts the wrong values of the critical indices. Another theoretical approach, the "scaling law" concept, which predicts relations among these indices, is described. The experimental evidence for and against the scaling laws is assessed. It is suggested that the scaling laws provide a promising approach to understanding phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.