A Schroedinger link between non-equilibrium thermodynamics and Fisher information

TL;DR

This paper demonstrates that both equilibrium and non-equilibrium thermodynamics can be derived from a Schrödinger wave equation framework based on Fisher information, unifying thermodynamics and quantum mechanics through an informational approach.

Contribution

It introduces a unified formalism where thermodynamics and quantum mechanics are both described by solutions to a Schrödinger wave equation derived from Fisher information extremization.

Findings

Equilibrium thermodynamics corresponds to the ground state of the SWE.

Non-equilibrium thermodynamics corresponds to excited states of the SWE.

Both thermodynamic regimes can be analyzed within a single Fisher information-based formalism.

Abstract

It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both non-equilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground state solution, and non-equilibrium thermodynamics corresponds to excited state solutions, of a Schroedinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium- and non-equilibrium 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.