Related papers: Towards a Geometry and Analysis for Bayesian Mecha…
In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential…
The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…
In these notes I explain the idea how one could understand confinement by studying the low energy effective dynamics of non Abelian gauge theories. I argue that under some mild assumptions, the low energy dynamics is determined universally…
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge…
We analyze an autonomous micro-engine as a closed quantum mechanical system, including the work it performs and the fuel it consumes. Our model system shows by example that it is possible to transfer energy steadily and spontaneously…
A central concept in active inference is that the internal states of a physical system parametrise probability measures over states of the external world. These can be seen as an agent's beliefs, expressed as a Bayesian prior or posterior.…
We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators…
We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity…
We consider quantum mechanical gauge theories with sixteen supersymmetries. The Hamiltonians or Lagrangians characterizing these theories can contain higher derivative terms. In the operator approach, we show that the free theory is…
In this paper, by arising condition in variation, from equal time to non-equal time, I reconsider how geometrodynamics equations allow to be derived from variational principle in general relativity and then find the variation of extrinsic…
Based only on classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike recent identities between…
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we…
The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
Biehl et al (2020) present some interesting observations on an early formulation of the free energy principle in (Friston, 2013). We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy…
A measurement can extract work from an entangled, e.g., two-mode system. Here, we inquire the extracted work when no intellectual creature, like an ancilla/daemon, is present. When the monitoring is carried out by the environmental modes,…
Topos formalism for quantum mechanics is interpreted in a broader, information retrieval perspective. Contexts, its basic components, are treated as sources of information. Their interplay, called daseinisation, defined in purely logical…
We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics. We present an algebra{statistics dictionary focused on statistical modeling. In particular, we link the…
Self-assembly kinetics is usually described by approaches which assume that the shape of the aggregates has a definite form (e.g., spherical, cylindrical, cubic, etc), however that is unlikely to be the case in many finite-sized…