Mathematical Aspects of Information Engine Theory

Information Engine is a physical system, which process informational signals and thereby produce work. In this light information can be considered as some kind of “fuel”. In this work we explore the main concepts of information engines. Firstly, we gave brief description of Maxwell Demon and Szilard Machine as the original model, which illustrate the main principles. The design of Maxwell’s Refrigerator illustrates the key points of the process with heat flow against the thermal gradient which is accompanied by writing some information. In the next part the opposite problem is given: transformation of some source of randomness into sample of other target distribution with the minimal thermodynamic “cost”. Finally, we explore econophysical model of wealth exchange in terms of informational engines and see that it is rather related to random numbers generation.