A universal theorem of sensory information

A universal theorem of sensory information, analogous to the second law of thermodynamics, is derived. Beginning from a minimal description of a sensory neuron, a state-space representation of firing rate emerges naturally from Shannon's measure of information. A special case of this formulation predicts a previously unknown inequality governing sensory adaptation, which was confirmed across different modalities, species, and experimental conditions. Further analysis shows that the firing rate behaves like a state function in thermodynamics, leading to an entropy production equation from which a general law follows: any closed cycle of stimulation yields a non-negative net gain of sensory information.