Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces

TL;DR

This work analyzes the thermostatistics of Yukawa and Lee–Wick potentials within a noncommutative (NC) phase space, employing Boltzmann-Gibbs statistics in both microcanonical and canonical ensembles. The NC structure, encoded by the parameter $\Theta$, deforms the phase-space volume and introduces $r^{-3}$ corrections to the potentials, modifying the density of states $g(E)$ and the partition function $Z(\beta)$ through first-order terms in $\Theta$. The authors derive explicit NC corrections to $g(E)$, inverse temperature relations, and partition functions, and compute the resulting mean energy and heat capacity, observing qualitative changes such as negative heat capacity in truncated regimes. The results highlight how NC geometry reshapes thermodynamics of short-range interactions and offer a framework to explore more complex systems, potential connections to quantum gravity, and the limits of semiclassical NC approaches.

Abstract

In recent years, physical models involving noncommutative algebras have attracted considerable interest since we can study theories with a Planck scale parameter which can seen as a semiclassical theory and consequently a path to a kind of quantum gravity. The noncommutative geometry introduces modifications to the underlying phase space structure, which can lead to new insights, and potentially solves outstanding problems in theoretical physics. In this work, we adopt a semiclassical perspective to perform a thermostatistical analysis of well-established potential models - Yukawa and Lee-Wick - within a noncommutative phase space. We obtain statistical thermodynamics quantities such as the density of states, partition function, average energy, and the heat capacity. We employ both the microcanonical and canonical ensemble formalisms, with the system embedded in a phase space modified by the noncommutativity of the space-time. We analyzed the negative heat capacities results obtained here in this noncommutativity scenario as a function of the modification of the microstructure of phase space thanks to the $θ$-parameter introduction. The entire treatment is conducted within the Boltzmann-Gibbs statistical mechanics framework.

Figures (8)

• Figure 1: Left panel : The plots of the pure Yukawa potential $(V_Y)$, the term with the noncommutative correction $(V_{NC})$, and the resulting potential $(V_{NCY})$ as functions of the radial distance $(r)$. Right panel : The NC Yukawa potential as function of the radial distance $(r)$, for the $\Theta$-values of $\Theta=0.3$, $\Theta=0.7$ and $\Theta=0.9$, in area unities
• Figure 2: Left panel : The plot of the pure term of the LW potential $(V_{LW})$, the term with the NC correction $(V_{NC})$, and the resulting potential $(V_{NCLW})$ as functions of the radial distance $(r)$. Right panel : The NC LW potential versus the radial distance $(r)$ for $\Theta=0$, $\Theta=0.1$, $\Theta=0.5$ and $\Theta=0.9$ in area unities.
• Figure 3: The partition function for the NC Yukawa potential as function of $\beta$ for $\Theta=0$, $\Theta=0.3$, $\Theta=0.7$, and $\Theta=0.9$ in area unities.
• Figure 4: The mean energy for the NCY potential as function of $\beta$. We use $\Theta=0$, $\Theta=0.3$, $\Theta=0.7$, and $\Theta=0.9$ in this plot in area unities.
• Figure 5: The heat capacity for the NC Yukawa potential as function of $\beta$ for the values of $\Theta=0$, $\Theta=0.3$, $\Theta=0.7$, and $\Theta=0.9$ in area unities.