Three thermodynamically-based parametrizations of the deceleration   parameter
  We propose, and constrain with the latest observational data, three model-independent parametrizations of the cosmic deceleration parameter $q(z)$. They are well behaved and stay finite at all redshifts. We construct them by fixing the value of $q$ at high redshift, $q(z \gg 1) = 1/2$ (as demanded by cosmic structure formation), and at the far future, $q(z = -1) = -1$, and smoothly interpolating $q(z)$ between them. The fixed point at $z = -1$ is not arbitrarily chosen; it readily follows from the second law of thermodynamics. This fairly reduces the ample latitude in parameterizing $q(z)$. 
Sergio del Campo, Ivan Duran, Ramon Herrera, and Diego Pavon
gr-qc astro-ph.CO