Non-Equilibrium Field Theory of Learning:

We present a unified theoretical framework that connects non-equilibrium

physical field equations to the fundamental limits and dynamics of learning

in both biological and artificial intelligence systems. Starting from a scalar

field G defined over matter of effective rest energy E and background potential

D, we derive a non-equilibrium chain rule:

dE

dt =

dG

dr ·

dr

dD ·

dD

dε ·

dε

dt.

We make three principal contributions. (I) We identify two physically distinct

roles in the chain: the composite structural term dG/dD = (dG/dr)(dr/dD),

fixed by system architecture, and the dynamic sensitivity dD/dε, controllable

during learning. (II) We define a Carnot-analogous learning efficiency

ηlearn =

dG

dD ·

dD

dε ≤

dG

dD ,

and prove that dG/dD constitutes an irrecoverable architectural ceiling that

no gradient-based algorithm can exceed. (III) We formalize the infant–adult

learning transition as a phase evolution of dD/dε from near-unity (maximum

plasticity) toward zero (crystallization), and propose the Sensitivity Field

Scheduler (SFS) as a concrete implementation. We further show that stan-

dard optimizers (SGD, Adam, cyclical learning rate) are limiting cases of SFS,

and that well-known empirical phenomena—neural scaling laws, the Lottery

Ticket Hypothesis, and grokking—receive natural interpretations within this

framework. Experimental protocols are proposed to validate the theory.