Does a Computer Have an Arrow of Time?

Abstract

Schulman (Entropy 7(4): [221][222][223][224][225][226][227][228][229][230][231][232][233] 2005) has argued that Boltzmann's intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed.

One-way-ness in the input-saving (Turing) machine

“…As Bennett's Turing machine operates adiabatically, such an erasure in reverse performed with an entropy increase in memory must be compensated by an entropy decrease of the measured system (see more detail in the Appendix). This means that Landauer's principle in reverse about information erasure violates the second law of thermodynamics and provokes time reversal in the measured system because entropy is the only physical quantity that requires an arrow of time [21,[28][29][30][31][32][33]. Thus, an input-saving machine cannot complete its backward cycle in polynomial-time, which implies that its controlled-NOT-based quantum circuit is one-way inside adiabatic thresholds.…”

“…Such a controlled-NOT operation is conceived to be mathematically embodied in an information heat engine, the feedback controller of which manipulates the measured system (an adiabatic box) based on its thermal fluctuations into its logical memory (a heat reservoir) to restore its standard state [13][14][15][16][17][18][19][20][21][22][23].…”

“…By Landauer's principle, this erasure is accompanied by heat generation into the adiabatic box, so that at the end of the full computational path, the net balance of entropy results in a minimal increase of entropy, S ≥ k B Log (2), in the measured system, where k B is the Boltzmann constant [12][13][14][15][16][17][18][19][20][21][22][23]. As a consequence, the entropy increase of the measured system is compensated by an entropy decrease of the random data, rendering the operation as a whole thermodynamically reversible.…”

“…2(d ′ ) displays. However, this would be like data being erased in the memory at zero thermodynamic cost, which Landauer's principle prevents [20][21][22][23][24]. Second, one may quasi-statically move the partition toward the far left side of the box, as Fig.…”

Time and irreversibility in axiomatic thermodynamics

“…Maroney attempted to show in 2010 that the logical operations involved in computation do not per se determine an arrow of time. 5 But in a 2014 rejoinder, Smith claimed that in the brain computational processes and in particular the formation of long-term memories in fact requires the existence of certain spontaneous diffusion/equilibration processes. 6 From the point of view of statistical mechanics, these processes correspond to local entropy increase.…”