Crossover of Scaling Behaviors of Work Cumulants in a Driven Gaussian Field Theory
Abstract
We derive the finite-temperature characteristic function of work (CFW) for a driven O(N) Gaussian field theory and obtain closed-form expressions for all zero-temperature excess-work cumulants. For gapped protocols, we use adiabatic perturbation theory (APT) to derive the τQ−2 scaling for protocols with a nonzero first derivative at either boundary, where τQ is the protocol duration; smoother boundaries lead to faster decay. For power-law protocols approaching the critical point with exponent p, we determine the competition between critical excitations and the regular contribution. The nth cumulant's critical contribution follows Kibble--Zurek (KZ) scaling τQ−p(d+n)/(p+2) for d+n<2p+4, acquires a logarithmic correction τQ−2plogτQ at d+n=2p+4, and scales as τQ−2p above this condition, where d is the spatial dimension. This analytical study of the APT--KZ crossover in a solvable model provides a basis for studying their competition in interacting field theories.
Related
- Boolean Cumulants and Exact Reduced Descriptions of Renewal-Driven Systems
- Glassy dynamics, crossover temperature and density scaling in fragile glass-formers
- Inclination-Induced Crossover in the Velocity Scaling of Lubrication-Mediated Droplet Motion
- Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain
- Scaling Density Functional Theory with Gaussian Splatting
BibTeX
@misc{qiao2026crossover,
title = {{Crossover of Scaling Behaviors of Work Cumulants in a Driven Gaussian Field Theory}},
author = {Yanbo Qiao and Ruohan Xu and H. T. Quan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36476},
eprint = {2609.36476},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36476},
}
RIS
TY - UNPB
TI - Crossover of Scaling Behaviors of Work Cumulants in a Driven Gaussian Field Theory
AU - Yanbo Qiao
AU - Ruohan Xu
AU - H. T. Quan
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36476
UR - https://arxiv.org/abs/2609.36476
AB - We derive the finite-temperature characteristic function of work (CFW) for a driven O(N) Gaussian field theory and obtain closed-form expressions for all zero-temperature excess-work cumulants. For gapped protocols, we use adiabatic perturbation theory (APT) to derive the τ_Q^−2 scaling for protocols with a nonzero first derivative at either boundary, where τ_Q is the protocol duration; smoother boundaries lead to faster decay. For power-law protocols approaching the critical point with exponent p, we determine the competition between critical excitations and the regular contribution. The nth cumulant's critical contribution follows Kibble--Zurek (KZ) scaling τ_Q^−p(d+n)/(p+2) for d+n<2p+4, acquires a logarithmic correction τ_Q^−2plogτ_Q at d+n=2p+4, and scales as τ_Q^−2p above this condition, where d is the spatial dimension. This analytical study of the APT--KZ crossover in a solvable model provides a basis for studying their competition in interacting field theories.
ER -