A comparative study of algorithms to find information entropy in equilibrium and non-equilibrium systems.*

The second law of thermodynamics establishes the concept of entropy as an observable physical quantity. However, while the use of the statistical-mechanical definition of entropy is common for equilibrium systems, there is no well-established expression for non-equilibrium systems. In order to address this challenge, we look into a generalized definition of entropy from an information theory perspective. A few recent studies [1-2] have indicated the possibility of quantifying the information density and applying it to simple systems to understand them qualitatively as well as quantitatively.

In the present work, we propose to discuss different algorithms to explore their scope in identifying phase transitions, ordering, and aggregation in real-time molecular dynamics simulation trajectories. In this process, we calculate the computable information density (CID) [3] with different algorithms and compare the results in different systems.

 

[1] Mengjie Zu et al J. Stat. Mech. (2020), 023204.

[2] Desgranges, C., and Delhommelle, J. J. Chem. Phys., (2020), 153, 224113.

[3] Martiniani, S., Chaikin, P. M., and Levine, D. Phys. Rev. X, (2019),  9, 011031.