One of the primary motivations of the research in the field of computation is to optimize the cost of computation. The major ingredient that a computer needs is the energy to run a process, i.e., the thermodynamic cost. The analysis of the thermodynamic cost of computation is one of the prime focuses of research. It started back since the seminal work of Landauer where it was commented that the computer spends kB T ln2 amount of energy to erase a bit of information (here T is the temperature of the system and kB represents the Boltzmanns constant). The advancement of statistical mechanics has provided us the necessary tool to understand and analyze the thermodynamic cost for the complicated processes that exist in nature, even the computation of modern computers. The advancement of physics has helped us to understand the connection of the statistical mechanics (the thermodynamics cost) with computation. Another important factor that remains a matter of concern in the field of computer science is the error correction of the error that occurs while transmitting the information through a communication channel. Here in this article, we have reviewed the progress of the thermodynamics of computation starting from Landauers principle to the latest model, which simulates the modern complex computation mechanism. After exploring the salient parts of computation in computer science theory and information theory, we have reviewed the thermodynamic cost of computation and error correction. We have also discussed about the alternative computation models that have been proposed with thermodynamically cost-efficient.
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