From Inference to Physics

Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system as it moves from given initial to final states. For an appropriately chosen configuration space the path of maximum probability reproduces Newtonian dynamics.

💡 Research Summary

The paper advances the program of Entropic Dynamics (ED), which seeks to derive the laws of physics from purely probabilistic and entropic rules for processing information. The authors begin by formulating a general framework in which the state of a physical system is represented by a point in a configuration space of informational variables. In this space the notion of distance is defined by the entropy‑based metric of information geometry, so that transitions between nearby states are governed by the principle of maximum entropy. By discretizing time into infinitesimal steps, they write the probability of a specific trajectory as a product of conditional probabilities for each step. Each conditional probability is taken to be a Gaussian whose variance is fixed by the entropy‑distance minimization, leading to a local “transition kernel” that depends on a parameter identified as the mass (m).

Summing the logarithms of these kernels over the entire trajectory yields an expression of the form

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