[Paper Review] Emergent quantum mechanics as a classical, irreversible thermodynamics

D. Acosta, Pedro Fernández de Córdoba+2 more|arXiv (Cornell University)|Jun 21, 2012

Advanced Thermodynamics and Statistical Mechanics36 references3 citations

TL;DR

This paper proposes a direct correspondence between semiclassical quantum mechanics and classical irreversible thermodynamics, showing that quantum propagators and path integrals emerge naturally from thermodynamic probability distributions in Gaussian, linear-response regimes. The key result is that quantum mechanics can be interpreted as an emergent phenomenon arising from classical thermodynamics, with action symmetry replaced by entropy in the underlying dynamics.

ABSTRACT

We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e., an effective description of some underlying degrees of freedom.

Motivation & Objective

• To establish a concrete, explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics, particularly in the Gaussian (linear response) approximation.
• To demonstrate that quantum mechanical concepts—such as propagators, path integrals, and wavefunctions—can be reinterpreted as thermodynamic quantities in a dissipative, stochastic framework.
• To provide independent support for the conjecture that quantum mechanics is not fundamental but emergent, by showing its formalism arises from classical thermodynamics.
• To explore the deeper implications of this correspondence, including the emergence of spacetime and the ontological status of quantum uncertainty.
• To lay the foundation for extending this mapping beyond the semiclassical limit into nonlinear irreversible thermodynamics.

Proposed method

• Mapping irreversible Gaussian Markov processes in thermodynamics to the semiclassical approximation of quantum mechanics via a stochastic process framework.
• Using the Chapman–Kolmogorov equation in both quantum mechanics and thermodynamics to establish a shared dynamical structure.
• Deriving quantum propagators from thermodynamic probability distributions using the Fokker–Planck and Fokker–Planck–Kolmogorov equations in the linear regime.
• Reconstructing the Feynman path integral from thermodynamic transition probabilities, showing its natural emergence in irreversible processes.
• Establishing a duality between mechanical action and entropy through a symmetry principle, replacing unitary evolution with dissipative, irreversible dynamics.
• Applying the correspondence to specific systems (e.g., free particle, harmonic oscillator), verifying exact agreement between thermodynamic and quantum expressions in the Gaussian limit.

Experimental results

Research questions

• RQ1 Can quantum mechanical propagators and path integrals be derived from the formalism of classical irreversible thermodynamics?
• RQ2 To what extent does the semiclassical approximation of quantum mechanics correspond to the linear-response regime of irreversible thermodynamics?
• RQ3 How does the symmetry between action and entropy underlie the emergence of quantum behavior from classical thermodynamic processes?
• RQ4 What does the correspondence imply about the ontological status of quantum mechanics—could it be emergent rather than fundamental?
• RQ5 Can spacetime and quantum concepts be seen as emergent from a deeper thermodynamic framework, given the mapping of spatial variables to thermodynamic variables?

Key findings

• Quantum mechanical propagators in the semiclassical limit are isomorphic to thermodynamic transition probabilities in irreversible, Gaussian Markov processes.
• The Feynman path integral arises naturally from the stochastic path description in irreversible thermodynamics, without postulating quantum principles.
• The time evolution of wavefunctions in quantum mechanics corresponds to the relaxation of thermodynamic distributions toward equilibrium, with the same mathematical structure.
• A fundamental symmetry between mechanical action and entropy is established, replacing unitary evolution with dissipative, irreversible dynamics.
• The correspondence holds exactly for free particles and harmonic oscillators in the Gaussian approximation, with explicit agreement between thermodynamic and quantum expressions.
• The mapping implies that quantum mechanics is not a fundamental theory but an emergent description, with spacetime and quantum uncertainty arising from underlying thermodynamic irreversibility.