Going Round in Circles: Landauer vs. Norton on the Thermodynamics of Computation

Algorithmic information theory in conjunction with Landauer’s principle can quantify the cost of maintaining a reversible real-world computational system distant from equilibrium. As computational bits are conserved in an isolated reversible system, bit flows can be used to track the way a highly improbable configuration trends toward a highly probable equilibrium configuration. In an isolated reversible system, all microstates within a thermodynamic macrostate have the same algorithmic entropy. However, from a thermodynamic perspective, when these bits primarily specify stored energy states, corresponding to a fluctuation from the most probable set of states, they represent “potential entropy”. However, these bits become “realised entropy” when, under the second law of thermodynamics, they become bits specifying the momentum degrees of freedom. The distance of a fluctuation from equilibrium is identified as the number of computational bits that move from stored energy states to momentum states to define a highly probable or typical equilibrium state. When reversibility applies, from Landauer’s principle, it costs k B l n 2 T Joules to move a bit within the system from stored energy states to the momentum states.

Section: Landauer’s Principlementioning

confidence: 99%

Algorithmic Entropy and Landauer’s Principle Link Microscopic System Behaviour to the Thermodynamic Entropy

Devine

2018

“…The values of A(n), A (n), A (n) for different input sets. 5 Based on the information from Table 2, it is seen that A (n) is a linear function of n, and it might be expected that A(n) is given by a · n 2 + b · n + c. Indeed, A(n) is represented as:…”

Section: A New View On the Insertion-sort Proceduresmentioning

confidence: 99%

“…Here, we assume (according to [5]) that: "Implementation means that a physical system is taken to represent abstract mathematical or logical states"; however, we do not take a part in the discussion about reversible nor irreversible computations and whether they can be physically implemented in procedure. The paper is concluded in Section 6, where we show some open questions and further work that can be done for better understanding algorithms' behavior.…”

Section: Introductionmentioning

confidence: 99%

Selected Remarks about Computer Processing in Terms of Flow Control and Statistical Mechanics

Strzałka

2016

Despite the fact that much has been said about processing in computer science, it seems that there is still much to do. A classical approach assumes that the computations done by computers are a kind of mathematical operation (calculations of functions values) and have no special relations to energy transformation and flow. However, there is a possibility to get a new view on selected topics, and as a special case, the sorting problem is presented; we know many different sorting algorithms, including those that have complexity equal to O(n lg(n)), which means that this problem is algorithmically closed, but it is also possible to focus on the problem of sorting in terms of flow control, entropy and statistical mechanics. This is done in relation to the existing definitions of sorting, connections between sorting and ordering and some important aspects of computer processing understood as a flow that are not taken into account in many theoretical considerations in computer science. The proposed new view is an attempt to change the paradigm in the description of algorithms' performance by computational complexity and processing, taking into account the existing references between the idea of Turing machines and their physical implementations. This proposal can be expressed as a physics of computer processing; a reference point to further analysis of algorithmic and interactive processing in computer systems.

“…According to this line of thinking, the thesis is grounded in the Second Law of thermodynamics (or its statistical mechanical counterparts). This is the prevalent approach, both in arguments supporting Landauer’s thesis (including e.g., [ 26 , 27 , 39 , 40 , 41 , 42 , 43 ]) and in arguments criticizing it (including e.g., [ 29 , 39 , 44 , 45 , 46 ]). (The connection between information, entropy and probability is also under dispute: see [ 47 , 48 ]).…”

Section: Introductionmentioning

confidence: 99%

Maxwell’s Demon in Quantum Mechanics

Shenker

Hemmo

2020

Maxwell’s Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to “exorcise” the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell’s Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer’s thesis, are not general. In this paper we demonstrate that Maxwell’s Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of “macrostates”, thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere.