Holographic complexity for Lifshitz system
Sourav Karar, Sunandan Gangopadhyay
TL;DR
This paper computes the holographic complexity for a Lifshitz spacetime, relating changes in complexity to energy and entanglement chemical potential, and explores how these relations resemble thermodynamic laws.
Contribution
It introduces a method to calculate holographic complexity in Lifshitz systems and relates it to thermodynamic quantities, extending previous holographic complexity studies.
Findings
Complexity change relates to energy and chemical potential variations.
Relations resemble the first law of thermodynamics.
Results hold for different dynamical exponents z.
Abstract
The holographic complexity of a 3+1-dimensional Lifshitz spacetime having a scaling symmetry is computed. The change in the holographic complexity between the excited state and the ground state is then obtained. This is then related to the changes in the energy and the entanglement chemical potential of the system. The calculation is carried out for both the values of the dynamical scaling exponent z in the Lifshitz spacetime. The relations has a very similar form to the corresponding relation involving the change in entanglement entropy known to be an analogous relation to the first law of thermodynamics.
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