Loschmidt's paradox
|
|
Loschmidt's paradox states that if there is a motion of a system that leads to a steady decrease of H (increase of entropy) with time, then there is certainly another allowed state of motion of the system, found by time reversal, in which H must increase.
This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with the second law of thermodynamics which describes the behavior of macroscopic systems. Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict; hence the paradox.
| Contents |
Arrow of time
One possible resolution of Loschmidt's paradox is to hypothesize that there is a so-called arrow of time in the Universe. One possible mechanism for an arrow of time is to assume that time itself is defined by changes in cosmic entropy; another is to assume that low-level violations of time reversal symmetry at the particle physics level are somehow driving cosmic entropy changes.
Out of disorder
A simpler resolution of the paradox can be found if the second law of thermodynamics is not seen as absolute; rather, less a law than a guideline. If the law is revised to state that entropy tends to increase over time, a different universe emerges, in which entropy may increase in both directions of time.
The usual example is a glass or other easily breakable object. Consider a point in time where the glass is intact, perhaps in falling to the ground. This is an ordered state for the glass; it may easily remain in this state indefinitely, but once broken it cannot be put back together. Upon reaching the ground, the glass shatters: this is its disordered state.
Consider the numerous ways in which the glass may break. It may simply chip, it may break into a few pieces, it may shatter into innumerable tiny fragments. Clearly, the glass has many disordered states, compared to its one ordered state. Over time, it is inevitable that the glass will fall into one of these states, as its ordered state is only one out of many possibilities. It can be seen that ordered states tend to become disordered.
Generally, this is where speculation on the nature of thermodynamics ends, as it has been demonstrated that entropy will increase. There is another possible conclusion, however.
Brought to a proper temperature, silica or glass will melt and can be shaped. Logically, this is the origin of our unfortunate glass. Consider the shattered glass: its fragments may be collected and melted, causing its molecules to become increasingly disordered from heat. The molten glass may then be formed into a new glass, identical (or nearly so) to the original glass. As the glass cools, its molecules become more ordered.
The falling glass is once again in an ordered state. Viewing time backwards, the glass warms until it melts and loses its shape entirely. As with its shattering, there are many ways in which the glass may melt. Once again it is inevitable that the glass will transition to one of these states: there are more of them.
Loschmidt's paradox vanishes. Regardless of the direction of time, ordered states tend to become disordered. It may be said that even as order becomes disorder, order arises out of disorder.
Fluctuation theorem
The fluctuation theorem proved by Evans (http://rsc.anu.edu.au/~evans/) and Searles (http://chem.sci.gu.edu.au/staff/d_bernhardt_personal.html) provides the final resolution of Loschmidt's paradox. The theorem is proved with the exact time reversible dynamical equations of motion and the axiom of causality. The fluctuation theorem is proved utilizing the fact that dynamics is time reversible. Quantitative predictions of this theorem have been confirmed in laboratory experiments conducted by Sevick (http://rsc.anu.edu.au/~sevick/groupwebpages/) et. al. using optical tweezers apparatus.
See also
External links
- Reversible laws of motion and the arrow of time (http://www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture_3/node2.html) by Mark Tuckerman