Thermodynamic and joint entropy of linear dissipative systems

Ronit Mahapatra

Physica A: Statistical Mechanics and its Applications, 2025, vol. 678, issue C

Abstract: We investigate the thermodynamic and information-theoretic aspects of an isolated linear dissipative system by analysing the damped harmonic oscillator. The thermodynamic entropy is obtained from the partition function, and its time evolution shows a consistent increase due to dissipation. Additionally, we evaluate Leipnik’s joint entropy and Fisher information using the wavefunction derived from the system’s propagator. We observe that in isolated dissipative systems, the presence of nonconservative dynamics leads to a decrease in the joint entropy and increase in Fisher information over time due to the time-dependent commutation relation. We have compared that with the Caldirola–Kanai model, where thermodynamic entropy remains constant and joint entropy is oscillatory. In the undamped limit, the results reduce to those of the simple harmonic oscillator, in which the entropy remains constant.

Keywords: Partition function; Entropy; Damped harmonic oscillator; Leipnik’s joint entropy; Fisher information; Cramer–Rao inequality (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:678:y:2025:i:c:s0378437125005692

DOI: 10.1016/j.physa.2025.130917

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