Abstract
Computations implemented on a physical system are fundamentally limited by the laws of physics. A prominent example for a physical law that bounds computations is the Landauer principle. According to this principle, erasing a bit of information requires a concentration of probability in phase space, which by Liouville's theorem is impossible in pure Hamiltonian dynamics. It therefore requires dissipative dynamics with heat dissipation of at least $k_BT\log 2$ per erasure of one bit. Using a concrete example, we show that when the dynamic is confined to a single energy shell it is possible to concentrate the probability on this shell using Hamiltonian dynamic, and therefore to implement an erasable bit with no thermodynamic cost.
Highlights
In 1961, Landauer established a remarkable relation between information theory and thermodynamics, by arguing that an irreversible computation cannot be made without any energetic cost [1]
Such an operation cannot be done in an isolated, Hamiltonian dynamic, Landauer concluded that implementing an erasable bit requires a dissipative system
In this paper we present an exactly solvable example of a classical Hamiltonian system that can serve as a memory bit, which is erasable at no energetic cost
Summary
In 1961, Landauer established a remarkable relation between information theory and thermodynamics, by arguing that an irreversible computation cannot be made without any energetic cost [1]. Landauer’s principle is famously known as the statement that an erasure of one bit of information—the hallmark of irreversible computations—must dissipate at least kBT log 2 of heat, where kB is the Boltzmann constant and T is the temperature of its surrounding environment This bound is rooted in the dissipative dynamic, enforced by the contraction of the physical system’s phase-space volume during the bit erasure. Additional generalizations of Landauer’s principle include other types of thermodynamic resources such as an angular momentum bath [4], a bound for entropically unbalanced bits [5], unifying the cost of erasing and measuring the bit [6,7], taking into account the mutual information between the bit and the bath [8], N state bit [9], finite time erasure [10,11], and others [12] All these generalizations, rely exclusively on dissipative dynamics: following Landauer’s argument, no energy conserving classical bit was suggested.
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