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

TL;DR

This paper presents a thermodynamical derivation of the quantum potential within Bohmian mechanics, linking it to an informational degree of freedom and associating a temperature with the wave function, exploring its behavior in various scenarios.

Contribution

It introduces a novel thermodynamical approach to derive the quantum potential by incorporating an informational degree of freedom, connecting thermodynamics with quantum mechanics.

Findings

Quantum potential derived using thermodynamics principles

A temperature can be associated with the wave function

Behavior of this temperature analyzed in different situations

Abstract

In this paper a thermodynamical derivation of the quantum potential is pro- posed. 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 temper- ature to each wave function. Features and behavior of this temperature in different situations is studied.