Addressing the Hubble Tension: Insights from Reversible and Irreversible Thermodynamic Processes

We investigate reversible and irreversible thermodynamic processes in cosmology and their impact on the Hubble tension. Gravitationally induced adiabatic matter creation/annihilation is treated as irreversible, while energy exchange between the cosmic bulk and horizon is modeled as reversible. Two scenarios are proposed: Model I features matter creation/annihilation across all species with energy transfer to effective entropic dark energy; Model II considers dark matter creation/annihilation with energy flow from baryonic matter and radiation. The creation rate is parameterized as $\mathrm{\Gamma }(t)={\mathrm{\Gamma }}_{0}H$, with energy transfer controlled by $\gamma$. We constrain both models using Pantheon$+$ supernovae, CMB distance priors, baryon acoustic oscillations, gamma-ray bursts, and cosmic chronometers, with and without SH${}_0$ES. When SH${}_0$ES is included, matter annihilation (${\mathrm{\Gamma }}_0<0$) is statistically preferred, yielding $H_0=71.75\pm 0.79$ km s${}^{-1}$ Mpc${}^{-1}$ (Model I) and $H_0=71.06\pm 0.81$ km s${}^{-1}$ Mpc${}^{-1}$ (Model II), corresponding to $1.2\sigma$ and $1.8\sigma$ consistency with the SH${}_0$ES value $73.17\pm 0.86$ km s${}^{-1}$ Mpc${}^{-1}$. Matter creation (${\mathrm{\Gamma }}_0>0$) or pure energy flow ($\mathrm{\Gamma }=0$) do not improve the tension. Without SH${}_0$ES, information criteria show no preference over $\mathrm{\Lambda }$CDM. For the matter annihilation/creation with energy flow, the effective entropic dark energy evolves dynamically, mimicking radiation and matter before recombination and approaching a cosmological constant at late times. These results demonstrate that thermodynamically motivated interactions can alleviate the Hubble tension when calibrated with local measurements, while remaining consistent with cosmological data.