Abstract
The authors analyze the minimal thermodynamic costs involved in performing computations using Turing machines. The resulting costs demonstrate the connections between statistical physics and algorithmic information theory.
Highlights
The relationship between thermodynamics and information processing has been an important area of research since at least the 1960s, when Landauer proposed that any process which erases a bit of information must release at least kT ln 2 of heat into its environment [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
In this paper we extend this line of research by deriving new results on the thermodynamic costs of performing general computations, as formalized by the notion of Turing machines (TMs)
We show that the heat function of the coin-flipping realization of a given TM is proportional to (x) minus a “correction term” which reflects the logically irreversibility of the input-output map computed by the TM
Summary
The relationship between thermodynamics and information processing has been an important area of research since at least the 1960s, when Landauer proposed that any process which erases a bit of information must release at least kT ln 2 of heat into its environment [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. TMs are a keystone of the theory of computation [46] and touch on several foundational issues that lie at the intersection of mathematics and philosophy, such as whether P = NP and Gödel’s incompleteness theorems [47] Their importance is partly due to the celebrated Church-Turing thesis, which postulates that any function that can be computed by a sequence of formal operations can be computed by some TM [48,49,50]. The Kolmogorov complexity of a string y, written as K (y), is the length of the shortest input program which causes a UTM to produce y as the output (formal definitions are provided in Sec. II B). Many of our results relate logical properties and thermodynamic costs at the level of individual computational trajectories (i.e., individual runs of the TM), which goes beyond most existing research on thermodynamics of computation
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