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arXiv:2101.04803 · International Journal of Quantum Chemistry

Information and thermodynamic properties of a non‐Hermitian particle ensemble

Francisco Cleiton E. Lima, Allan R. P. Moreira, Carlos Alberto S. Almeida

Published Feb 26, 2021• 23 citations
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Abstract

Abstract In the context of non‐relativistic quantum mechanics, we investigated Shannon's entropy of a non‐Hermitian system to understand how this quantity is modified with the cyclotron frequency. Subsequently, we turn our attention to the construction of an ensemble of these spinless particles in the presence of a uniform magnetic field. Then, we study the thermodynamic properties of the model. Finally, we show how Shannon's entropy and thermodynamic properties are modified with the action of the magnetic field.

DOI
10.1002/qua.26645

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We calculate the Fisher information (Fr and Fp) and the Shannon entropies (Sr and Sp) of a spinless charged particle in three different configurations of time-varying magnetic field, B(t). To do so, we first obtain the exact wave functions for a general time-dependent system by using a dynamical invariant method. By considering the solutions for n = m = 0, we were able to obtain the expressions of Fr, Fp, Sr, and Sp in terms of a c-number quantity, ρ, which has to be a real solution of the Milne–Pinney equation. We observe that the inequality FrFp ≤ 16 holds for the systems considered. We also observed squeezing phenomenon in momentum or/and coordinate spaces with increasing time.
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In this study, we uncover the intrinsic information processes in non-Hermitian quantum systems and their thermodynamic effects. We demonstrate that these systems can exhibit negative entropy production, making them potential candidates for information engines. We also identify a key informational quantity that can characterize phase transitions beyond the reach of traditional partition functions. This work enhances our understanding of the interplay between information and thermodynamics, providing a new perspective on non-Hermitian quantum systems.
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