Loschmidt's paradox
In
Origin
Reversible laws of motion cannot explain why we experience our world to be in such a comparatively low state of entropy at the moment (compared to the equilibrium entropy of universal heat death); and to have been at even lower entropy in the past.
Before Loschmidt
In 1874, two years before the Loschmidt paper,
Arrow of time
Any process that happens regularly in the forward direction of time but rarely or never in the opposite direction, such as entropy increasing in an isolated system, defines what physicists call an
Although most of the arrows of time described by physicists are thought to be special cases of the thermodynamic arrow, there are a few that are believed to be unconnected, like the cosmological arrow of time based on the fact that the universe is expanding rather than contracting, and the fact that a few processes in particle physics actually violate time-symmetry, while they respect a related symmetry known as CPT symmetry. In the case of the cosmological arrow, most physicists believe that entropy would continue to increase even if the universe began to contract[citation needed] (although the physicist Thomas Gold once proposed a model in which the thermodynamic arrow would reverse in this phase). In the case of the violations of time-symmetry in particle physics, the situations in which they occur are rare and are only known to involve a few types of meson particles. Furthermore, due to CPT symmetry, reversal of the direction of time is equivalent to renaming particles as antiparticles and vice versa. Therefore, this cannot explain Loschmidt's paradox.
Dynamical systems
Current [
Abstract mathematical tools used in the study of dissipative systems include definitions of mixing, wandering sets, and ergodic theory in general.
Fluctuation theorem
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One approach to handling Loschmidt's paradox is the
There is a crucial point in the fluctuation theorem, that differs from how Loschmidt framed the paradox. Loschmidt considered the probability of observing a single trajectory, which is analogous to enquiring about the probability of observing a single point in phase space. In both of these cases the probability is always zero. To be able to effectively address this you must consider the probability density for a set of points in a small region of phase space, or a set of trajectories. The fluctuation theorem considers the probability density for all of the trajectories that are initially in an infinitesimally small region of phase space. This leads directly to the probability of finding a trajectory, in either the forward or the reverse trajectory sets, depending upon the initial probability distribution as well as the dissipation which is done as the system evolves. It is this crucial difference in approach that allows the fluctuation theorem to correctly solve the paradox.
Information theory
A more recent proposal concentrates on the step of the paradox in which velocities are reversed. At that moment the gas becomes an open system, and in order to reverse the velocities, position and velocity measurements have to been made.
Big Bang
Another way of dealing with Loschmidt's paradox is to see the second law as an expression of a set of boundary conditions, in which our universe's time coordinate has a low-entropy starting point: the
See also
- Maximum entropy thermodynamics for one particular perspective on entropy, reversibility and the Second Law
- Poincaré recurrence theorem
- Reversibility
- Statistical mechanics
References
- S2CID 119792996.
- Thomson, W. (Lord Kelvin) (1874/1875). The kinetic theory of the dissipation of energy, Nature, Vol. IX, 1874-04-09, 441–444.
- ISBN 0-7923-5564-4.
- ^ D. J. Evans and D. J. Searles, Adv. Phys. 51, 1529 (2002).
- ^ Sevick, Edith. "2002 RSC Annual Report - Polymers and Soft Condensed Matter". Research School of Chemistry. Australian National University. Retrieved 2022-04-01.
- .
- J. Loschmidt, Sitzungsber. Kais. Akad. Wiss. Wien, Math. Naturwiss. Classe 73, 128–142 (1876)
External links
- Reversible laws of motion and the arrow of time by Mark Tuckerman
- Toy systems with time-reversible discrete dynamics showing entropy increase Fibonacci Iterated Map ; Ising-Conway Game