  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 Boltzmann's
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 Landauer's 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.
