Entropic Dynamics

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 appropriate to the problem at hand. In this paper we review three examples of entropic dynamics. First we tackle the simpler case of a standard diffusion process which allows us to address the central issue of the nature of time. Then we show that imposing the additional constraint that the dynamics be non-dissipative leads to Hamiltonian dynamics. Finally, considerations from information geometry naturally lead to the type of Hamiltonian that describes quantum theory.

[1]  Gerhard Groessing.  The vacuum fluctuation theorem: Exact Schrödinger equation via nonequilibrium thermodynamics , 2008 .

[2]  Ariel Caticha,et al.  Consistency and Linearity in Quantum Theory , 1998, quant-ph/9803086.

[3]  Edward Nelson,et al.  Review of stochastic mechanics , 2012 .

[4]  Caslav Brukner,et al.  Information and Fundamental Elements of the Structure of Quantum Theory , 2002, quant-ph/0212084.

[5]  A. Caticha,et al.  Entropic dynamics and the quantum measurement problem , 2011, 1108.2550.

[6]  Domenico Giulini,et al.  The Physical Basis of the Direction of Time , 2008 .

[7]  Siegfried Fussy,et al.  The Quantum as an Emergent System , 2012, 1205.3393.

[8]  J. Skilling,et al.  Origin of complex quantum amplitudes and Feynman's rules , 2009, 0907.0909.

[9]  Amit Goswami,et al.  The Copenhagen Interpretation , 2001 .

[10]  Ariel Caticha,et al.  Momentum and uncertainty relations in the entropic approach to quantum theory , 2011 .

[11]  David T. Johnson.  Generalized Galilean Transformations and the Measurement Problem in the Entropic Dynamics Approach to Quantum Theory , 2011 .

[12]  Marcel Reginatto,et al.  Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information , 1998 .

[13]  Ariel Caticha,et al.  Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics , 2014 .

[14]  A. Caticha.  Entropic dynamics, time and quantum theory , 2010, 1005.2357.

[15]  Huw Price,et al.  Time's Arrow and Archimedes’ Point , 1997 .

[16]  Instituto de Física, Universidade Federal do Rio de Janeiro, Cidade Universitária, CT , 2002 .

[17]  Daniel C. Cole,et al.  The quantum dice: An introduction to stochastic electrodynamics , 1996 .

[18]  Ariel Caticha,et al.  Entropic Dynamics: an inference approach to quantum theory, time and measurement , 2014, 1403.3822.

[19]  Gerard 't Hooft,et al.  Emergent quantum mechanics and emergent symmetries , 2007, 0707.4568.

[20]  Edward Nelson,et al.  Connection between Brownian motion and quantum mechanics , 1979 .

[21]  T. Wallstrom.  On the derivation of the Schrödinger equation from stochastic mechanics , 1989 .

[22]  W. Wootters.  Statistical distance and Hilbert space , 1981 .

[23]  T. Takabayasi,et al.  Vortex, spin and triad for quantum mechanics of spinning particle. I General theory) , 1983 .

[24]  R. Spekkens.  Evidence for the epistemic view of quantum states: A toy theory , 2004, quant-ph/0401052.

[25]  Michael J. W. Hall,et al.  Schrödinger equation from an exact uncertainty principle , 2001 .

[26]  H. Elze,et al.  Emergent discrete time and quantization: relativistic particle with extra-dimensions , 2003 .

[27]  Lee Smolin.  Could quantum mechanics be an approximation to another theory , 2006 .

[28]  Shahid Nawaz.  Momentum and spin in entropic quantum dynamics , 2014 .

[29]  Stephen L. Adler,et al.  Quantum Theory as an Emergent Phenomenon: Introduction and overview , 2004 .