We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players’ point of view.
Preparing thermal (Gibbs) states is a common task in physics and computer science. Recent algorithms mimic cooling via system-bath coupling, where the cost is determined by mixing time, akin to classical Metropolis-like algorithms. However, few methods exist to demonstrate slow mixing in quantum systems, unlike the well-established classical tools for systems like the Ising model and constraint satisfaction problems. We present a quantum generalization of these tools through a generic bottleneck lemma that implies slow mixing in quantum systems. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles and quantified either through Bohr spectrum jumps or operator locality. Using our bottleneck lemma, we establish unconditional lower bounds on the mixing times of Gibbs samplers for several families of Hamiltonians at low temperatures. For classical Hamiltonians with mixing time lower bounds
Tmix=exp[Ω(nα)], we prove that quantum Gibbs samplers also have
Tmix=exp[Ω(nα)]. This applies to models like random
K-SAT instances and spin glasses. For stabilizer Hamiltonians, we provide a concise proof of exponential lower bounds
Tmix=exp[Ω(n)] on mixing times of good
n-qubit stabilizer codes at low constant temperature. Finally, we consider constant-degree classical Hamiltonians and show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques. We show generic results for models with linear free energy barriers, and we demonstrate that our techniques extend to models with sublinear free energy barriers by proving
Tmix=exp[n1/2−o(1)] for the ferromagnetic 2D transverse field Ising model.
Energy-ordered occupation is deeply embedded in quantum physics, from the Aufbau principle governing the filling of electronic states in atoms and molecules to the emergence of low-energy configurations in quantum many-body systems. However, the dynamical mechanism by which a generic quantum state develops such an energy hierarchy remains a fundamental question. Here we show that such an energy hierarchy can emerge dynamically from nonlinear quantum dissipation. Rather than being imposed as a principle or generated through coupling to a thermal reservoir, an Aufbau-like ordering of energy levels emerges intrinsically under quantum Landau-Lifshitz-Gilbert dynamics from a generic initial mixed state. This convergence is a nontrivial consequence of Lyapunov monotonicity and instability of disordered population configurations. The resulting dynamics establish an intrinsic nonlinear mechanism for organizing density-matrix populations and provides a route toward selective preparation of low-energy subspaces. Numerical simulations confirm analytical predictions and illustrate convergence toward low-energy sectors.