Editing T-symmetry (section)

== Macroscopic phenomena ==
===The second law of thermodynamics===

[[Image:teeter-totter.png|frame|A toy called the [[teeter-totter]] illustrates, in cross-section, the two aspects of time reversal invariance. When set into motion atop a pedestal (rocking side to side, as in the image), the figure oscillates for a very long time. The toy is engineered to minimize friction and illustrate the reversibility of [[Newton's laws of motion]]. However, the mechanically stable state of the toy is when the figure falls down from the pedestal into one of arbitrarily many positions. This is an illustration of the law of increase of [[entropy]] through [[Boltzmann]]'s identification of the logarithm of the number of states with the entropy.]]

Daily experience shows that T-symmetry does not hold for the behavior of bulk materials. Of these macroscopic laws, most notable is the [[second law of thermodynamics]]. Many other phenomena, such as the relative motion of bodies with friction, or viscous motion of fluids, reduce to this, because the underlying mechanism is the dissipation of usable energy (for example, kinetic energy) into heat.

The question of whether this time-asymmetric dissipation is really inevitable has been considered by many physicists, often in the context of [[Maxwell's demon]]. The name comes from a [[thought experiment]] described by [[James Clerk Maxwell]] in which a microscopic demon guards a gate between two halves of a room. It only lets slow molecules into one half, only fast ones into the other. By eventually making one side of the room cooler than before and the other hotter, it seems to reduce the [[entropy]] of the room, and reverse the arrow of time. Many analyses have been made of this; all show that when the entropy of room and demon are taken together, this total entropy does increase. Modern analyses of this problem have taken into account [[Claude E. Shannon]]'s relation between [[information entropy|entropy and information]]. Many interesting results in modern computing are closely related to this problem—[[reversible computing]], [[quantum computing]] and [[physical limits to computing]], are examples. These seemingly metaphysical questions are today, in these ways, slowly being converted into hypotheses of the physical sciences.

The current consensus hinges upon the Boltzmann–Shannon identification of the logarithm of [[phase space]] volume with the negative of [[information theory|Shannon information]], and hence to [[entropy]]. In this notion, a fixed initial state of a macroscopic system corresponds to relatively low entropy because the coordinates of the molecules of the body are constrained. As the system evolves in the presence of [[dissipation]], the molecular coordinates can move into larger volumes of phase space, becoming more uncertain, and thus leading to increase in entropy.

=== Big Bang===
One resolution to irreversibility is to say that the constant increase of entropy we observe happens ''only'' because of the initial state of our universe. Other possible states of the universe (for example, a universe at [[Heat death of the Universe|heat death]] equilibrium) would actually result in no increase of entropy. In this view, the apparent T-asymmetry of our universe is a problem in [[physical cosmology|cosmology]]:  why did the universe start with a low entropy? This view, supported by cosmological observations (such as the [[isotropy]] of the [[cosmic microwave background]]) connects this problem to the question of ''initial conditions'' of the universe.

===Black holes===
The laws of gravity seem to be time reversal invariant in classical mechanics; however, specific solutions need not be.

An object can cross through the [[event horizon]] of a [[black hole]] from the outside, and then fall rapidly to the central region where our understanding of physics breaks down. Since within a black hole the forward light-cone is directed towards the center and the backward light-cone is directed outward, it is not even possible to define time-reversal in the usual manner. The only way anything can escape from a black hole is as [[Hawking radiation]].

The time reversal of a black hole would be a hypothetical object known as a [[white hole]]. From the outside they appear similar. While a black hole has a beginning and is inescapable, a white hole has an ending and cannot be entered. The forward light-cones of a white hole are directed outward; and its backward light-cones are directed towards the center.

The event horizon of a black hole may be thought of as a surface moving outward at the local speed of light and is just on the edge between escaping and falling back. The event horizon of a white hole is a surface moving inward at the local speed of light and is just on the edge between being swept outward and succeeding in reaching the center. They are two different kinds of horizons—the horizon of a white hole is like the horizon of a black hole turned inside-out.

The modern view of black hole irreversibility is to relate it to the second law of thermodynamics, since black holes are viewed as [[Black hole thermodynamics|thermodynamic objects]]. For example, according to the [[gauge–gravity duality]] conjecture, all microscopic processes in a black hole are reversible, and only the collective behavior is irreversible, as in any other macroscopic, thermal system.{{Citation needed|date=April 2010}}

===Kinetic consequences: detailed balance and Onsager reciprocal relations===

In physical and [[chemical kinetics]], T-symmetry of the mechanical microscopic equations implies two important laws: the principle of [[detailed balance]] and the [[Onsager reciprocal relations]]. T-symmetry of the microscopic description together with its kinetic consequences are called [[microscopic reversibility]].

===Effect of time reversal on some variables of classical physics===

====Even====
Classical variables that do not change upon time reversal include:
:<math>\vec x</math>, position of a particle in three-space
:<math>\vec a</math>, acceleration of the particle
:<math>\vec F</math>, force on the particle
:<math>E</math>, energy of the particle
:<math>V</math>, electric potential (voltage)
:<math>\vec E</math>, electric field
:<math>\vec D</math>, electric displacement
:<math>\rho</math>, density of electric charge
:<math>\vec P</math>, electric polarization
:[[Energy density]] of the electromagnetic field
:<math>T_{ij}</math>, [[Maxwell stress tensor]]
:All masses, charges, coupling constants, and other physical constants, except those associated with the weak force.

====Odd====
Classical variables that time reversal negates include:
:<math>t</math>, the time when an event occurs
:<math>\vec v</math>, velocity of a particle
:<math>\vec p</math>, linear momentum of a particle
:<math>\vec l</math>, angular momentum of a particle (both orbital and spin)
:<math>\vec A</math>, electromagnetic vector potential
:<math>\vec B</math>, magnetic field
:<math>\vec H</math>, magnetic auxiliary field
:<math>\vec j</math>, density of electric current
:<math>\vec M</math>, magnetization
:<math>\vec S</math>, [[Poynting vector]]
:<math>\mathcal{P}</math>, power (rate of work done).

====Example: Magnetic Field and Onsager reciprocal relations====
Let us consider the example of a system of charged particles subject to a constant external magnetic field: in this case the canonical time reversal operation that reverses the velocities and the time <math>t</math> and keeps the coordinates untouched is no more a symmetry for the system. Under this consideration, it seems that only Onsager–Casimir reciprocal relations could hold;<ref>{{cite journal |last1=Kubo |first1=Ryogo |title=Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems |journal=Journal of the Physical Society of Japan |date=15 June 1957 |volume=12 |issue=6 |pages=570–586 |doi=10.1143/JPSJ.12.570|bibcode=1957JPSJ...12..570K }}</ref> these equalities relate two different systems, one subject to <math>\vec B</math> and another to <math>-\vec B</math>, and so their utility is limited. However, it was proved that it is possible to find other time reversal operations which preserve the dynamics and so Onsager reciprocal relations;<ref>{{cite journal |last1=Bonella |first1=Sara |last2=Ciccotti |first2=Giovanni |last3=Rondoni |first3=Lamberto |title=Time reversal symmetry in time-dependent correlation functions for systems in a constant magnetic field |journal=EPL (Europhysics Letters) |date=2015 |volume=108 |issue=6 |page=60004 |doi=10.1209/0295-5075/108/60004|s2cid=121427119 }}</ref><ref>{{cite journal |last1=Luo |first1=Rongxiang |last2=Benenti |first2=Giuliano |last3=Casati |first3=Giulio |last4=Wang |first4=Jiao |title=Onsager reciprocal relations with broken time-reversal symmetry |journal=Physical Review Research |date=2020 |volume=2 |issue=2 |page=022009 |doi=10.1103/PhysRevResearch.2.022009|bibcode=2020PhRvR...2b2009L |doi-access=free }}</ref><ref>{{cite journal |last1=Carbone |first1=Davide |last2=Rondoni |first2=Lamberto |title=Necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields |journal=Symmetry |date=2020 |volume=12 |issue=8 |pages=1336 |doi=10.3390/sym12081336|arxiv=2008.05193 |bibcode=2020Symm...12.1336C |doi-access=free }}</ref> in conclusion, one cannot state that the presence of a magnetic field always breaks T-symmetry.