[Paper Review] Degenerate vacua from unification of second law of thermodynamics with other laws

H. B. Nielsen, Masao Ninomiya|ArXiv.org|Jan 3, 2007

Cosmology and Gravitation Theories7 references17 citations

TL;DR

This paper proposes a unified framework where the second law of thermodynamics emerges from a fundamental probability density functional over classical paths in phase space, leading to the prediction of multiple degenerate vacua with nearly zero cosmological constants. By treating coupling constants as dynamical variables, the model naturally realizes the Multiple Point Principle, predicting several vacua with vanishing effective energy densities, offering a novel unification of thermodynamics with quantum field theory and cosmology.

ABSTRACT

Using our recent attempt to formulate second law of thermodynamics in a general way into a language with a probability density function, we derive degenerate vacua. Under the assumption that many coupling constants are effectively ``dynamical'' in the sense that they are or can be counted as initial state conditions, we argue in our model behind the second law that these coupling constants will adjust to make several vacua all having their separate effective cosmological constants or, what is the same, energy densities, being almost the \underline{same} value, essentially zero. Such degeneracy of vacuum energy densities is what one of us works on a lot under the name "The multiple point principle" (MPP).

Motivation & Objective

• To unify the second law of thermodynamics with other physical laws by formulating it as a fundamental probability density functional over classical phase space paths.
• To explore whether the second law can emerge from a deeper dynamical principle that respects time-reversal and CPT symmetries.
• To investigate the cosmological consequences of such a formulation, particularly the prediction of multiple vacua with nearly degenerate, vanishing cosmological constants.
• To test the viability of the Multiple Point Principle (MPP) as a consequence of this unified thermodynamic framework.
• To provide a phenomenologically motivated mechanism for the smallness of the cosmological constant and the top quark mass via vacuum degeneracy.

Proposed method

• Formulate the second law as a probability density functional P(path) on phase space, assigning probabilities to classical solutions of the equations of motion.
• Use a general complex action formalism, allowing independent real and imaginary parts, to preserve time-reversal and CPT symmetries.
• Assume that coupling constants and mass parameters are dynamical, depending on fields or initial conditions, rather than fixed.
• Apply the probability functional to derive effective vacuum energy densities across different minima of the scalar field potential.
• Use the condition of degeneracy in vacuum energy densities (MPP) to constrain the Higgs and top quark masses.
• Predict observable signatures such as suppressed Higgs production rates at colliders, interpreted as 'hand of God' effects.

Experimental results

Research questions

• RQ1 Can the second law of thermodynamics be derived from a deeper, symmetry-preserving probability functional over classical paths in phase space?
• RQ2 Does assuming dynamical coupling constants lead to a natural prediction of multiple vacua with degenerate, near-zero cosmological constants?
• RQ3 Can the Multiple Point Principle emerge as a consequence of this unified thermodynamic framework rather than being postulated?
• RQ4 What are the phenomenological consequences of such a framework for the Higgs boson mass and top quark mass?
• RQ5 Are there testable 'hand of God' effects, such as suppressed Higgs production, predicted by this model?

Key findings

• The model predicts the existence of multiple degenerate vacua with nearly identical, vanishing effective cosmological constants, consistent with the Multiple Point Principle.
• The top quark mass is predicted to be approximately 173 GeV with a 6 GeV uncertainty, based on the assumption of three degenerate vacua in the Standard Model.
• The Higgs boson mass is predicted to be around 115 GeV/c², consistent with LEP data, after a correction from a previous estimate of 135 GeV/c².
• The model suggests that Higgs particles may be disfavored in production at colliders due to 'hand of God' effects, potentially testable at the LHC.
• The cosmological constant is predicted to be small and positive, with its value constrained by vacuum degeneracy, offering a solution to the hierarchy problem.
• The framework unifies the second law of thermodynamics with quantum field theory and cosmology by deriving thermodynamic behavior from a fundamental probability functional over classical paths.