2 Information thermodynamics encoder and encoding 2 . 1 Definition of information thermodynamics encoder

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 Y, specific sub-systems in an encoder X with internal correlations can exceed the information thermodynamics bound on (X,Y) and encode more information than system 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. Perhaps the connection between thermodynamics and information is one of the most intriguing relations discovered in physics. It is impressive to see the ubiquitous and critical roles of information thermodynamics links in diverse physical, chemical, and biological systems. Nowadays, emerging interests have arisen in studying information thermodynamics in complex systems (e.g., the human brain), whose complexity originates from heterogeneous elements and intricate internal correlations. An open challenge relates to the elusive roles of internal orders inside a complex system in influencing information thermodynamics. This research attempts to lay a cornerstone of this rising direction. We present a theory of the thermodynamics of encoding, where a non-isolated system X acts as an information thermodynamics encoder to encode the information of an external source Y through thermodynamics coupling. This theory reveals an intrinsic difference between the non-isolated system with intra-system coupling and the non-isolated system of independent elements in information thermodynamics characteristics. It demonstrates that a stronger internal correlation inside system X implies a higher possibility for specific sub-systems of X to encode more information of Y than X itself. We Thermodynamics of Encoding and Encoders A PREPRINT further verify the ubiquity of these findings in representative non-isolated systems in physics and biology, such as the Ising model with a random external field and the human brain, an ultra-complex system of neurons, during perception. These validated theoretical results may deepen our understanding of physical and biological information processing systems and inspire advanced computing architecture, storage infrastructure, and artificial neural network designs.