Fluctuations in Complex Systems

Statistical Mechanics forms the natural home for a systematic study of fluctuations in physical phenomena. When studying Equilibrium Statistical Mechanics, we proceed from the Microcanonical (describing an isolated system), through the Canonical (system in contact with a heat bath), to the Grand Canonical (system in contact with a heat and particle bath) ensembles. The systematic relaxation of requirements via introduction of appropriate heat and/or particle baths naturally gives rise to an analysis of fluctuations. Indeed, early experiments and theories of fluctuations concerned systems in the linear response regime close to thermal equilibrium, giving rise to such celebrated works as the Stokes-Einstein relation, the Fluctuation-Dissipation Theorem, and the Green-Kubo relations. Even in out-of-equilibrium systems where a notion of local equilibrium applies, one has access to general results such as Onsagers Reciprocal Relations. Alas, no equivalent general results are known as yet for systems strongly driven far from thermal equilibrium where extreme fluctuations are witnessed on account of nonlinear interactions and/or strong correlations. Yet, most natural phenomena fall in this latter category. Similar to Tolstoy’s quote in Anna Karenina, Happy families are all alike; every unhappy family is unhappy in its own way, thus far it seems all equilibrium fluctuations are alike for similar reasons, whereas non-equilibrium fluctuations are each distinct for their own specific reasons. In the absence of general guiding principles, the only approach to non-equilibrium fluctuations for now, seems to be to take up a systematic study of disparate systems and collate ones understanding of their fluctuations as well as the underlying causes of those fluctuations. In this talk, I will explain a few case studies in a few non-equilibrium phenomena we are currently studying in my group, and will continue in future. These systems/phenomena include:

1) Turbulence: Power and thrust spectra in propeller based air and underwater locomotion.
2) Frustrated amorphous media: Percolation mechanisms en route to jamming of loose granular packs.
3) Interfacial Flows: Marangoni flows at air-water interfaces induced by surface tension gradients.
Time permitting, I will also discuss my interests in bio-inspired problems in:
4) Evolution of the human foot.
5) Social colony behaviour of garden eels.
6) Neural coding of species identity in birdsong prosody.