https://doi.org/10.1140/epjb/s10051-025-01072-4
Regular Article - Statistical and Nonlinear Physics
Extracting equilibrium information from the non-equilibrium phenomena of sparsely placed water molecules undergoing a finite-time cyclic process
1
Department of Physics, Wolkite University, Wolkite, Ethiopia
2
Center for Engineering, Modeling and Applied Social Sciences, Federal University of ABC, Sao Paulo, Brazil
3
Department of Physics, Dire Dawa University, Dire Dawa, Ethiopia
4
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
Received:
9
July
2024
Accepted:
6
October
2025
Published online:
27
October
2025
In this work, we consider a large number of water molecules placed on a lattice far apart, so that they are very weakly interacting with each other and are in contact with a heat bath at temperature T. A strong static electric field, 
, is applied to these molecules along the z-axis, causing a three-level energy splitting. A weak alternating electric field, applied in the 
plane for a finite-time 
, induces transitions between these three levels. This weak alternating field acts as a time-dependent protocol 
, which is switched on at 
and off at 
. The same cyclic process is repeated for a large number of times. The data available for this finite-time non-equilibrium process allow us to extract equilibrium thermodynamic quantities, such as the difference in free energy between the final and initial states of the system. We analytically obtain the work distributions and analyze the average work of the three-level system as a function of 
and time around the optimum frequency, where is the frequency of the alternating electric field. Furthermore, our theoretical framework is further validated through Monte Carlo simulations, which confirm the fidelity of extracting equilibrium free-energy differences and the consistency with the Jarzynski equality.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
