Extracting equilibrium information from the non-equilibrium phenomena of sparsely placed water molecules undergoing a finite-time cyclic process

Yigermal Bassie (), Mohammed Mahmud, André Kazuo Takahata and Mulugeta Bekele
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Yigermal Bassie: Wolkite University
Mohammed Mahmud: Dire Dawa University
André Kazuo Takahata: Federal University of ABC
Mulugeta Bekele: Addis Ababa University

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 10, 1-10

Abstract: Abstract 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, $$E_{0}$$ E 0 , is applied to these molecules along the z-axis, causing a three-level energy splitting. A weak alternating electric field, applied in the $$xy-$$ x y - plane for a finite-time $$\tau $$ τ , induces transitions between these three levels. This weak alternating field acts as a time-dependent protocol $$\zeta (t)$$ ζ ( t ) , which is switched on at $$t=0$$ t = 0 and off at $$t=\tau $$ t = τ . 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 $$\omega $$ ω and time around the optimum frequency, where $$\omega $$ ω 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. Graphic abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-01072-4

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