Most systems that we see around us,  from inanimate machines that do useful work  to living biological systems, function far from equilibrium. They are characterized by a  continuous, non vanishing heat dissipation into the environment which contributes to an overall rate of increase of the entropy of the universe.  This rate of heat dissipation or rate of entropy production is a measure of how far from equilibrium a system is.

Non-equilibrium systems also exist at the microscopic scales, in our cells as molecular motors, as dissipative components  in computer chips and as  living micro organisms. For e.g., the Kinesin protein shown in the Figure, which belongs to a class of motor proteins in eukaryotic cells, moves along microtubule filaments powered by the hydrolysis of adenosine triphosphate (ATP).


Kinesin walks along a microtubule by the hydrolysis of ATP. Recent research from Fysikum aims to develop analytical tools for estimating the energy dissipated at these microscopic scales. Image courtesy:


Compared to macroscopic systems, where the dissipation is caused by a large number of degrees of freedom, microscopic systems are often described by only a few degrees of freedom.
However, even so, measuring entropy production at such small scales, is typically hard to do: its a quantity which is small in magnitude as well as a quantity which is fluctuating. Existing analytical results are very few and current computational schemes usually require vast amounts of data. In recent work,  we have  overcome this hurdle by proposing a new scheme for estimating entropy production in small systems by analyzing short time series data, collected from a small non-equilibrium system as it evolves in time [1] . This new method only needs several very short time series to work, making it easier to apply  to different experimental settings as compared to existing schemes which typically require several very long time series measurements.
That such a scheme should work was originally motivated by exact solutions of mathematical models, but has since then been proven rigorously.

This work is part of the PhD thesis work of Sreekanth K. Manikandan in collaboration with postdoctoral fellow Deepak Gupta at the University of Padua, and supervised by Supriya Krishnamurthy.

In future work we want  to further develop and use this method in different experimental settings, where  standard methods are either very challenging or even fail. Some of the experimental settings that we are considering include active matter systems, Friction force microscopy experiments and particles in hydrodynamic flows.


[1] Inferring Entropy Production from Short Experiments
Sreekanth K. Manikandan, Deepak Gupta, and Supriya Krishnamurthy
Phys. Rev. Lett. 124, 120603  (2020)