BCAM Scientific Seminar: Nonequilibrium thermodynamics, cross-correlations, and the isoperimetric inequality

We have recently proved an inequality for Markovian stochastic processes, which has implications for nonequilibrium thermodynamics and biophysics. This inequality concerns the "cross-correlation", i.e., the covariance between distinct observables measured at two different points in time. Cross-correlations play an important role in statistical physics: according to the principle of "microscopic reversibility", cross-correlations in equilibrium are symmetric under exchange of observables. Violations of this symmetry present a fundamental, empirically accessible, and often-used statistical signature of deviation from equilibrium. 

Our inequality relates the asymmetry of cross-correlations and the thermodynamic affinity (i.e., the strength of nonequilibrium driving). This allows us to derive thermodynamic bounds on functional properties that depend on such asymmetry. It also suggests a way to infer affinity from empirical measurements, in a different manner to so-called "thermodynamic uncertainty relations" which have recently attracted attention in the field. Interestingly, and somewhat surprisingly, our inequality is proved by using the isoperimetric inequality, which relates the area and perimeter of regular polygons.

As one illustration of our result, we prove a previously-conjectured bound on the coherence of noisy oscillations, as measured by the ratio of the imaginary and real parts of the eigenvalues of the Markovian generator.  As another illustration, we derive a thermodynamic bound on directed information flow in a model of biochemical signal transduction.

Joint work with Naruo Ohga and Sosuke Ito, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.077101