A thermodynamical derivation of the quantum potential and the temperature of the wave function

In this paper a thermodynamical derivation of the quantum potential is proposed. Within the framework of Bohmian mechanics we show how the quantum potential can be derived, by adding an additional informational degree of freedom to the ordinary degrees of freedom of a physical system. Such a derivation uses the First Law of thermodynamics for this additional degree of freedom and basic equilibrium thermodynamics methods. By doing that, one may associate a temperature to each wave function. Features and behavior of this temperature in different situations is studied. •We have proposed a thermodynamical derivation for the quantum potential.•We have investigated relation between the quantum potential and the Fisher information.•We have assigned a temperature to the wavefunction.