2018/03/31 by Daniel Nickelsen, Hugo Touchette
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Entropy (arrow of time) #Entropy production #Langevin equation #Large deviations theory #Limit (mathematics) #Mathematics #Non-equilibrium thermodynamics #Observable #Physics #Quantum mechanics #Scaling #Statistical Mechanics and Entropy #Statistical physics #Thermodynamic limit #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.121.090602
published as Phys. Rev. Lett. 121, 090602 (2018) · v1: 8 pages including supplementary material, 3 figures; v2: typos corrected, references added, close to published version; v3: $ξ$ corrected in 3 places. Correct value is $ξ=2/α$
openalex publication_date 2018/08/31 · arxiv created 2020/07/31 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time τ appears linearly, unless the process considered has long-range correlations, in which case τ is generally replaced by τξ with ξ≠1. Here, we show that such an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation. We describe the mechanism underlying this scaling using path integrals and discuss its physical consequences for more general processes.