A team proposes a definition of non-equilibrium Gibbsian entropy valid for general quantum systems, computable from Wigner functions for both Gaussian and non-Gaussian states. The formulation remains positive definite despite the Wigner function being a quasi-probability, and preserves fundamental results —the law of large numbers, the central limit theorem and the relation between entropy and the cumulant generating function— that underpin large deviation theory.

The entropy is defined from our ignorance of the underlying state structure after repeated measurements of cumulants, in parallel with the classical Gibbs formulation but applicable out of equilibrium. The authors also derive associated information theory quantities: relative entropy, conditional entropy, mutual information and Rényi entropy.

The formalism is compared with Wehrl entropy for the 1D harmonic oscillator, for both pure and mixed states. The work concludes by discussing potential applications, ranging from quantum correlations beyond entanglement to thermalization in closed quantum systems.