Related papers: H-theorem do-conjecture
A new representation of Game Theory is developed in this paper. State of players is represented by a density matrix, and payoff function is a set of hermitian operators, which when applied onto the density matrix give the payoff of players.…
We propose a classical solution for the kinetic description of matter falling into a black hole, which permits to evaluate both the kinetic entropy and the entropy production rate of classical infalling matter at the event horizon. The…
The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical probability laws. In this paper, a new quantum dynamic belief…
Statistical physics is important in understanding the physics of interacting many bodies. This has been historically developed by attempts to understand colliding gases and quantifying quantities like entropy, free energy, and other…
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…
Prompted by the realisation that the statistical entropy of an ideal gas in the micro-canonical ensemble should not fluctuate or change over time, the meaning of the H-theorem is re-interpreted from the perspective of information theory in…
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schr\"odinger equation is just the classical H-J equation, constrained by a condition that…
The paper contains the attempt to integration of the classical evolutionary game theory based on replicator dynamics and the state based approach of Houston and Mcnamara. In the new approach, individuals have different heritable strategies,…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results…
We develop the compositional theory of active inference by introducing activity, functorially relating statistical games to the dynamical systems which play them, using the new notion of approximate inference doctrine. In order to exhibit…
Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated.…
Since Newton's time, deterministic causality has been considered a crucial prerequisite in any fundamental theory in physics. In contrast, the present work investigates stochastic dynamical models for motion in one spatial dimension, in…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
Beginning with the Bell theorem, cyclic systems of dichotomous random variables have been the object of many foundational findings in quantum mechanics. Here, we ask the question: if one chooses a cyclic system "at random" (uniformly within…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
We discuss the possibility of deriving an H-theorem for the nonlinear discrete time evolution known as Ulam's redistribution of energy problem. In this model particles are paired at random and then their total energy is redistributed…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…