Entropy and Quantum Information

“In all of physical law, there’s arguably no principle more sacrosanct than the second law of thermodynamics — the notion that entropy, a measure of disorder, will always stay the same or increase.”

“But something about the second law troubles physicists.”

“Although it’s called a law, it’s usually regarded as merely probabilistic: It stipulates that the outcome of any process will be the most probable one”

“They may have woven the second law out of the fundamental principles of quantum mechanics — which, some suspect, have directionality and irreversibility built into them at the deepest level.”

“According to this view, the second law comes about not because of classical probabilities but because of quantum effects such as entanglement. It arises from the ways in which quantum systems share information, and from cornerstone quantum principles that decree what is allowed to happen and what is not.”

“In this telling, an increase in entropy is not just the most likely outcome of change. It is a logical consequence of the most fundamental resource that we know of — the quantum resource of information.”

“Thermodynamics was conceived in the early 19th century to describe the flow of heat and the production of work.”

“it became one of the central pillars of modern physics, providing criteria that govern all processes of change.”

“Entropy is loosely equated with disorder, but the Austrian physicist Ludwig Boltzmann formulated it more rigorously as a quantity related to the total number of microstates a system has: how many equivalent ways its particles can be arranged.”

“the second law implies that change must happen in a way that increases entropy.”

“This directionality is widely considered to impose an arrow of time. In this view, time seems to flow from past to future because the universe began — for reasons not fully understood or agreed on — in a low-entropy state and is heading toward one of ever higher entropy.”

“there’s no fundamental reason why entropy can’t decrease — why, for example, all the air molecules in your room can’t congregate by chance in one corner. It’s just extremely unlikely.”

“the laws of classical physics are deterministic — they allow only a single outcome for any starting point. Where, then, can that hypothetical ensemble of states enter the picture at all, if only one outcome is ever possible?”

“Constructor theory aims to express all of physics in terms of statements about possible and impossible transformations.”

“It echoes the way thermodynamics itself began, in that it considers change in the world as something produced by “machines” (constructors) that work in a cyclic fashion, following a pattern like that of the famous Carnot cycle, proposed in the 19th century to describe how engines perform work.”

“The constructor is rather like a catalyst, facilitating a process and being returned to its original state at the end.”

“just because a machine for conducting a certain task might exist, that doesn’t mean it can also undo the task.”

“This makes the operation of the constructor different from the operation of the dynamical laws of motion describing the movements of the bricks, which are reversible.”

“for most complex tasks, a constructor is geared to a given environment. It requires some specific information from the environment relevant to completing that task.”

“Irreversibility is not just the most probable outcome but the inevitable one, governed by the quantum interactions of the components.”

“Without quite realizing it, Maxwell connected the thermodynamic law to the issue of informatio”

“The demon has used information about the motions of molecules to apparently undermine the second law. Information is thus a resource that, just like a barrel of oil, can be used to do work.”

“Almost a century later, physicists proved that Maxwell’s demon doesn’t subvert the second law in the long term, because the information it gathers must be stored somewhere, and any finite memory must eventually be wiped to make room for more.”

“In 1961 the physicist Rolf Landauer showed that this erasure of information can never be accomplished without dissipating some minimal amount of heat, thus raising the entropy of the surroundings. So the second law is only postponed, not broken.”

“The informational perspective on the second law is now being recast as a quantum problem.”

“One of the most versatile ways to understand this new quantum version of thermodynamics invokes so-called resource theories — which again speak about which transformations are possible and which are not.”

“Quantum resource theories adopt the picture of the physical world suggested by quantum information theory, in which there are fundamental limitations on which physical processes are possible.”

“In quantum information theory these limitations are typically expressed as “no-go theorems”: statements that say “You can’t do that!””

“Resource theories have a few main ingredients. The operations that are allowed are called free operations.”

“A resource, meanwhile, is something that an agent can access to do something useful — it could be a pile of coal to fire up a furnace and power a steam engine. Or it could be extra memory that will allow a Maxwellian demon to subvert the second law for a little longer.”

“The resource-theory approach, said physicist Markus Müller of the University of Vienna, “admits a fully mathematically rigorous derivation, without any conceptual or mathematical loose ends, of the thermodynamic laws and more.””

“it is not so much about the average properties of large ensembles of moving particles, but about a game that an agent plays against nature to conduct a task efficiently with the available resources”

“In the end, though, it is still about information. The discarding of information — or the inability to keep track of it — is really the reason why the second law holds”