ICTS:28796

Video URL

A theory of randomness - II (Online) + Q&A

A theory of randomness - II (Online) + Q&A

(2024). A theory of randomness - II (Online) + Q&A. SciVideos. https://youtu.be/LesYfOYOgOc

A theory of randomness - II (Online) + Q&A. SciVideos, May. 29, 2024, https://youtu.be/LesYfOYOgOc 

          @misc{ scivideos_ICTS:28796,
            doi = {},
            url = {https://youtu.be/LesYfOYOgOc},
            author = {},
            keywords = {},
            language = {en},
            title = {A theory of randomness - II (Online) + Q\&A},
            publisher = {},
            year = {2024},
            month = {may},
            note = {ICTS:28796 see, \url{https://scivideos.org/icts-tifr/28796}}
          }
Jin-Song von Storch
Talk numberICTS:28796
Source RepositoryICTS-TIFR
Source EventTheoretical and Practical Perspectives in Geophysical Fluid Dynamics
Collection

Abstract

Consider a system described by a multi-dimensional state vector X. The evolution of x is governed by a set of equations in the form of dx/dt=F(X(t)). x is a component of X. F(X(t)), the differential forcing of x, is a deterministic function of X. The solution of such a system often exhibits randomness, where the solution at one time is independent of the solution at another time. This study investigates the mechanism responsible for such randomness. We do so by exploring the integral forcing of x, G_T (t), a definite integral of F over the time span extending from t to t+T, which links the solution at two times, t and t+T.

We show that, for a system in equilibrium, G_T (t) can be expressed as G_T (t)=c_T+d_T x(t)+f_T (t), which consists of (apart from constant c_T) a dissipating component with strength d_T and a fluctuating component f_T (t), in line with the fluctuation-dissipation theorem that for a system in equilibrium, anything that generates fluctuations must also damp the flu...