Thermodynamic transport inequality: Inferring dissipation from observed transport from single-molecule to bulk observables

Small biological systems are inherently stochastic due to thermal fluctuations. Inferring dissipation, that is, if and how far biological systems (or processes) are driven out of equilibrium, from fluctuating observations, which typically track only a small subset of degrees of freedom, remains a key challenge in modern non-equilibrium physics. While existing approaches have focused on how sample-to-sample fluctuations and correlations relate to, or are bounded by, dissipation, recent work from the Mathematical bioPhysics group shows that the average transport of a general observable already encodes information about the underlying non-equilibrium thermodynamics of all (including the hidden) degrees of freedom.

Transport phenomena are ubiquitous in biophysical systems and typically occur far from thermal equilibrium. The thermodynamic deviation from equilibrium is best quantified in terms of the entropy production, which encodes information about the energy that is required to drive or maintain the transport.

In a recent theoretical paper published in Physical Review Letters (Phys. Rev. Lett. 133, 067101 (2024)), Cai Dieball and Aljaz Godec from the Mathematical bioPhysics group at the Max Planck Institute for Multidisciplinary Sciences, Göttingen, derived an inequality that bounds  the thermodynamic entropy production using the average transport of a general observable. Compared to existing approaches, the new theory allows to rigorously estimate the displacement of a system from thermodynamic equilibrium solely from averages of fluctuating quantities, and thus applies not only to single-molecule but also to bulk observables and fully accounts for any inertial effects. This advance allows, for the first time, to bridge the gap between stochastic thermodynamics and established bulk experiments, such as time-resolved x-ray scattering, which can only observe dynamics averaged over a large ensemble of molecules.

Importantly, the novel transport inequality holds for a much broader class of stochastic dynamics than existing theory and thus also on a broader range of timescales, opening new avenues in the field of thermodynamic inference in small systems, such as light-driven soft matter, molecular and artificial nano-machines, or Brownian heat engines.