Spontaneous irreversibility and objective thermalization in stochastic modifications of quantum theory

TL;DR

This work argues that unitary quantum dynamics cannot generically realize irreversible equilibration for a single isolated system, proposing that quantum theory is an effective framework requiring corrections near the thermodynamic limit. It develops an objective quantum thermalization (OQT) model—a norm-preserving stochastic modification with a fluctuation-dissipation relation that drives ensembles toward a microcanonical equilibrium with rate ω = 2 α 𝒩 / ħ and entropy S_th = k_B log Ω, while preserving energy. It then blends OQT with objective collapse into Spontaneous Universal Irreversibility (SUI), introducing simultaneous thermalization and state reduction via two generators, Λ_χ and Λ_R, producing a hybrid steady state ρ_∞ that interpolates between Born statistics and microcanonical behavior. The framework yields a falsifiable, agent-independent mechanism for quantum irreversibility and quantum-to-classical transition in the thermodynamic limit, with potential experimental tests in mesoscopic systems and implications for foundational questions in quantum statistical mechanics.

Abstract

The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation employ subjective restrictions on the space of observables or states and do not explain how a single macroscopic quantum system achieves equilibrium dynamically. We instead argue that quantum theory is an effective theory and requires corrections to accurately describe systems approaching the thermodynamic limit. We construct a stochastic extension of quantum theory which is practically identical to quantum mechanics for microscopic systems, yet allows single, isolated macroscopic systems to objectively thermalize, generically. A fluctuation-dissipation relation guarantees physical consistency including norm preservation, energy conservation, no superluminal signalling and the emergence of microcanonical equilibrium. We further discuss the inclusion of objective collapse, thereby realizing a falsifiable theory of spontaneous universal irreversibility which describes the quantum-to-classical crossover dynamics of macroscopic quantum systems. The dynamics of the model describe spontaneous symmetry breaking, quantum state reduction and objective quantum thermalization for individual systems while realizing an emergent hybrid statistics for ensembles which interpolates between Born's rules and microcanonical equilibrium.

Figures (1)

• Figure 1: Time evolution of observable expectation values, $\langle\hat{O}\rangle=\mathrm{Tr}[\hat{\rho}\,\hat{O}]$, where $\hat{\rho}$ follows Eq. \ref{['Eq:Therm_master_Final']} and the effective strength of the modification, $\tilde{\alpha}:=\alpha\,\mathcal{N}/\hbar$ is interpolated. When $\tilde{\alpha} = 0$ (dark blue), standard quantum theory is recovered, while $\tilde{\alpha} >0$ (dark red, orange and light blue in decreasing order) is the OQT regime which show deviations from the purely oscillatory effects of standard quantum dynamics while observable expectation values thermalize. (a) Evolution of expectation values of $\hat{O}_1:= |i\rangle\langle j| + |j\rangle\langle i|$ where $i,j$ label energy eigenstates within the microcanonical subspace. Note, $\hat{O}_1$ thermalizes although it is not an ETH observable. (b) Evolution of expectation values of $\hat{O}_2$, a random Hermitian observable, chosen to showcase generic deviations from standard quantum predictions. Numerical analysis used $\mathrm{dim}\,\mathcal{H}=25$ (complex) with time-steps, $dt=10^{-4}$. $\hat{H}$ was chosen with random discrete spectrum in $[0.0,10.0]$, with a regular mean level spacing and standard deviation $0.01$. The initial state was a random pure state constituting a Gaussian in the energy basis amplitudes, its mean being far from the ground state and a large spread with standard deviation $0.2$.