The study of computation is paramount to the discipline of computer science.
Comparison to calculation
Calculation is a term for the computation of numbers, while computation is a wider reaching term for information processing in general.
A computation can be seen as a purely physical phenomenon occurring inside a closed physical system called a computer. Examples of such physical systems include digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, analog computers or wetware computers. This point of view is the one adopted by the branch of theoretical physics called the physics of computation.
Accounts of computation
The mapping account
A classic account of computation is found throughout the works of Hilary Putnam and others. Peter Godfrey-Smith has dubbed this the “simple mapping account.” Gualtiero Piccinini's summary of this account states that a physical system can be said to perform a specific computation when there is a mapping between the state of that system to the computation such that the “microphysical states [of the system] mirror the state transitions between the computational states.”
The semantic account
Philosophers such as Jerry Fodor have suggested various accounts of computation with the restriction that semantic content is a necessary condition for computation (that is, that what differentiates an arbitrary physical system from a computing system is that the operands of the computation represent something). This notion attempts to prevent the logical abstraction of the mapping account of pancomputationalism, or the idea that everything can be said to be computing everything.
The mechanistic account
Gualtiero Piccinini proposes an account of computation based in mechanical philosophy. It states that physical computing systems are types of mechanisms that, by design, perform physical computation, or “the manipulation (by a functional mechanism) of a medium-independent vehicle according to a rule.” Medium-independence allows for the use of physical variables with traits other than voltage (as in typical digital computers); this is imperative in considering other types of computation, such as that that occurs in the brain or in a quantum computer. A rule, in this sense, provides a mapping among inputs, outputs, and internal states of the physical computing system. 
- State models including Turing machine, pushdown automaton, finite state automaton, and PRAM
- Functional models including lambda calculus
- Logical models including logic programming
- Concurrent models including actor model and process calculi
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- Physical information
- Real computation
- Reversible computation
- Computation from the Free Merriam-Webster Dictionary
- Godfrey-Smith, P. (2009), "Triviality Arguments against Functionalism", Philosophical Studies, 145 (2): 273–95
- Piccinini, Gualtiero (2015). Physical Computation: A Mechanistic Account. Oxford: Oxford University Press. p. 17. ISBN 9780199658855.
- Fodor, J. A. (1981), "The Mind-Body Problem", Scientific American, 244 (January 1981)
- Piccinini, Gualtiero (2015). Physical Computation: A Mechanistic Account. Oxford: Oxford University Press. p. 10. ISBN 9780199658855.