Related papers: Knowledge as a Breaking of Ergodicity
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical…
Establishing a description for confinement is not something simple. In order to try to understand a little about this phenomenon, we will explore the thermodynamics of models that try to describe it in terms of propagators with violation of…
Thermodynamics could be seen as an expression of physics at a high epistemic level. As such, its potential as an inductive bias to help machine learning procedures attain accurate and credible predictions has been recently realized in many…
Foundational Machine Learning Potentials can resolve the accuracy and transferability limitations of classical force fields. They enable microscopic insights into material behavior through Molecular Dynamics simulations, which can crucially…
A short introduction on quantum thermodynamics is given and three new topics are discussed: 1) Maximal work extraction from a finite quantum system. The thermodynamic prediction fails and a new, general result is derived, the ``ergotropy''.…
We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site…
From the nano-scale to the macro-scale, biological tissue is spatially heterogeneous. Even when tissue behavior is well understood, the exact subject specific spatial distribution of material properties is often unknown. And, when…
Heat capacities of model systems with finite numbers of effective degrees of freedom are evaluated using canonical and microcanonical thermodynamics. Discrepancies between both approaches, which are observed even in the infinite-size limit,…
We present here for the first time a unifying perspective for the lack of equipartition in non-linear ordered systems and the low temperature phase-space fragmentation in disordered systems. We demonstrate that they are just two…
Stochastic thermodynamics allows us to define heat and work for microscopic systems far from thermodynamic equilibrium, based on observations of their stochastic dynamics. However, a complete account of the energetics necessitates that all…
The excess free energy functional of classical density functional theory depends upon the type of fluid model, specifically on the choice of (pair) potential, is unknown in general, and is approximated reliably only in special cases. We…
When using deep, multi-layered architectures to build generative models of data, it is difficult to train all layers at once. We propose a layer-wise training procedure admitting a performance guarantee compared to the global optimum. It is…
Energy-based models (EBMs) are flexible generative architectures inspired by statistical physics, but their learning and generative properties remain poorly understood. Here, we analyze a solvable EBM in the high-dimensional limit: the…
The metabolic processes complexity is at the heart of energy conversion in living organisms and forms a huge obstacle to develop tractable thermodynamic metabolism models. By raising our analysis to a higher level of abstraction, we develop…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the…
When does society eventually learn the truth, or take the correct action, via observational learning? In a general model of sequential learning over social networks, we identify a simple condition for learning dubbed excludability.…
Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…
A fundamental problem in quantum thermodynamics is to properly quantify the work extractable from out-of-equilibrium systems. While for closed systems, maximum quantum work extraction is defined in terms of the ergotropy functional, this…
In this paper we explore the richness of information captured by the latent space of a vision-based generative model. The model combines unsupervised generative learning with a task-based performance predictor to learn and to exploit…