We phenomenologically derive a cosmological model that includes both a cosmological constant term $\mathrm{\Lambda }/3$ and a dissipative driving term $\beta (2H^2+\dot{H})$ by applying both the first law of thermodynamics and an effective entropy (that is proportional to the Bekenstein-Hawking entropy) to matter creation cosmology. Here $H$, $\dot{H}$, and $\beta$ are the Hubble parameter, the time derivative of $H$, and a non-negative dimensionless coefficient used for the effective entropy, respectively. The dissipative term is proportional to the Ricci scalar curvature, suggesting that the dynamic creation pressure has the same dependence. We examine the model’s background evolution in the late universe and its horizon thermodynamics. The present model supports a transition from a decelerating universe to an accelerating universe when $\beta <0.5$. The second law of thermodynamics is always satisfied on the horizon, and maximization of entropy is satisfied in the final stage. In addition, we study first-order density perturbations related to structure formation, by applying a neo-Newtonian approach to the present model. We then examine constraints on the present model using three types of observational data and the transitional and thermodynamic constraints and find that a weakly dissipative universe with $\mathrm{\Lambda }$ is likely favored and consistent with our Universe. We also discuss irreversible entropy due to adiabatic particle creation, assuming a holographiclike matter creation cosmology.

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• Dark energy
• Evolution of the Universe