Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schrödinger equation follows naturally from information geometry.

Abstract. Entropic Dynamics (ED) is a framework that allows the formulation of dynamical theories as an application of entropic methods of inference. In the generic application of ED to derive the Schrödinger equation for N particles the dynamics is a non-dissipative diffusion in which the system follows a "Brownian" trajectory with fluctuations superposed on a smooth drift. We show that there is a family of ED models that differ at the "microscopic" or sub-quantum level in that one can enhance or suppress the fluctuations relative to the drift. Nevertheless, members of this family belong to the same universality class in that they all lead to the same emergent Schrödinger behavior at the "macroscopic" or quantum level. The model in which fluctuations are totally suppressed is of particular interest: the system evolves along the smooth lines of probability flow. Thus ED includes the Bohmian or causal form of quantum mechanics as a special limiting case. We briefly explore a different universality class -a nondissipative dynamics with microscopic fluctuations but no quantum potential. The Bohmian limit of these hybrid models is equivalent to classical mechanics. Finally we show that the Heisenberg uncertainty relation is unaffected either by enhancing or suppressing microscopic fluctuations or by switching off the quantum potential.

An Entropic Dynamics of exchange rates is laid down to model the dynamics of foreign exchange rates, FX, and European Options on FX. The main objective is to represent an alternative framework to model dynamics. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. Entropic Dynamics is an application of entropic inference, which is equipped with the entropic notion of time to model dynamics. The scale invariance is a symmetry of the dynamics of exchange rates, which is manifested in our formalism. To make the formalism manifestly invariant under this symmetry, we arrive at choosing the logarithm of the exchange rate as the proper variable to model. By taking into account the relevant information about the exchange rates, we derive the Geometric Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under the scale transformation. Securities should be valued such that there is no arbitrage opportunity. To this end, we derive a risk-neutral measure to value European Options on FX. The resulting model is the celebrated Garman-Kohlhagen

Abstract. In the Entropic Dynamics (ED) derivation of the Schrödinger equation the physical input is introduced through constraints that are implemented using Lagrange multipliers. There is one constraint involving a "drift" potential that correlates the motions of different particles and is ultimately responsible for entanglement. The purpose of this work is to deepen our understanding of the corresponding multiplier α . We find that α must take integer values. Its main effect is to control the strength of the drift relative to the fluctuations. We show that ED exhibits a symmetry: models with different values of α can lead to the same Schrödinger equation; different "microscopic" or sub-quantum models lead to the same "macroscopic" or quantum behavior. In the limit of large α the drift prevails over the fluctuations and the particles tend to move along the smooth probability flow lines. Thus ED includes the causal or Bohmian form of quantum mechanics as a special limiting case.

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock's price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock's price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker-Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the * mabedi@albany.edu † dbartolomeo@albany.edu risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black-Scholes model and the Black-Scholes-Merton differential equation are derived.