The Shannon entropy dependence on temperature, dipole moment and thermodynamic properties of microtubules (MTs) have been investigated using the Landau–Ginzburg phenomenological theory through continuum Boltzmann distribution function. By minimising the loss in energy, we found that there is a possibility that MTs formed from the heterodimers can process information over a long time at higher temperature. We also found that multiple heterodimers under the influence of dipole moment, has the tendency to process information whenever the amount of information stored or transferred decreases with increasing electronegativity of the system. We analyse the dynamic instability phenomenon that infinitely occurs in polymerisation and depolymerisation processes in MTs. Also, under physiological conditions, temperature dependence of thermodynamic properties was investigated and our results exhibited critical behaviour of heat capacity and chemical potential giving room for phase transitions around 302 K.