Schrödinger link between nonequilibrium thermodynamics and Fisher information

Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):046128. doi: 10.1103/PhysRevE.66.046128. Epub 2002 Oct 22.

Abstract

It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both nonequilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground-state solution, and nonequilibrium thermodynamics corresponds to excited-state solutions, of a Schrödinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium and nonequilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis. As an application, we discuss viscosity in dilute gases.