Thermodynamics of Encoding and Encoders.

Non-isolated systems have diverse coupling relations with the external environment. These relations generate complex thermodynamics and information transmission between the system and its environment. The framework depicted in the current research attempts to glance at the critical role of the internal orders inside the non-isolated system in shaping the information thermodynamics coupling. We characterize the coupling as a generalized encoding process, where the system acts as an information thermodynamics encoder to encode the external information based on thermodynamics. We formalize the encoding process in the context of the nonequilibrium second law of thermodynamics, revealing an intrinsic difference in information thermodynamics characteristics between information thermodynamics encoders with and without internal correlations. During the information encoding process of an external source $\mathsf{Y}$, specific sub-systems in an encoder $\mathsf{X}$ with internal correlations can exceed the information thermodynamics bound on $\left(\mathsf{X},\mathsf{Y}\right)$ and encode more information than system $\mathsf{X}$ works as a whole. We computationally verify this theoretical finding in an Ising model with a random external field and a neural data set of the human brain during visual perception and recognition. Our analysis demonstrates that the stronger internal correlation inside these systems implies a higher possibility for specific sub-systems to encode more information than the global one. These findings may suggest a new perspective in studying information thermodynamics in diverse physical and biological systems.