posted 31. January 2007 05:27                    

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It seems kind of intuitive that for a system with few particles that they can sometimes scatter into a microstate of higher probability (lower entropy).

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The quote did not refer to a multiparticle system, but rather to a single nanomachine or protein motor. They are not talking about intermolecular motions relative to a laboratory reference system, but rather intra molecular motions with motion relative to the nanomachine itself. IOW, "classical thermodynamics does not apply to these small systems" because this is not a kinetic system. The "thermal energy available per degree of freedom" refers to the bond energy, vibrational and rotational, of nanomachines and protein motors. The study you speak of equates entropy with energy flow, and disorder with energy dissipation. IOW a switch is made from a particle interpretation to an energy interpretation.

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Does the Fluctuation Theorem satisfy conservation laws?

The theoretical foundations of the fluctuation theorem are defined by the kinetic theory of gases. This has led, in an interpretation of a laser trap experiment, to premature claims of second law violations1. To see why kinetic theory does not give an accurate description of the experiment consider the case of liquid helium. In the superfluid state helium forms a Bose-Einstein condensate such that the atoms are considered identical. Therefore the canonical variables (qi,pi) are inadequate for describing the state of the system and cannot in principle be used for applications of the second law. A more accurate assessment is obtained by applying energy equipartition and using the canonical variables of energy and time (E,t). As energy flows through the system it disperses by distributing itself uniformly among the available degrees of freedom and microstates. Because energy dissipates as it flows it provides a description of increasing entropy that is complementary to the second law. Both laws must be satisfied when assessing a steady state system. If equipartition is now applied to the solvent-particle system, with relaxation times and hydrogen bonding occurring at rates on the order of picoseconds, then theory suggests that a two second trajectory cannot be caused by thermal collisions because energy imbalances are resolved much too quickly. Thus in order to ensure the validity of the conservation laws there must be an undetected energy flow (E,t) in addition to the molecular kinetic flow (qi,pi).

The colloidal particle diameter of 6.3 μm is at the upper limit for Brownian motion yet its random motions in the trap are clearly visible. Since exponential laws are common in nature there may be forces present which augment the Brownian motion due to molecular collisions. An electrostatic influence may exist that acts upon the polar bonds of the solvent; the laser may cause superfluorescence to occur by exciting electrons within the colloidal particle; or damped oscillation due to intermolecular forces may cause a mechanical effect that influences the particle's motion. To investigate these possibilities variations of the laser trap experiment should be performed, such as; changing the temperature of the solvent; using a nonpolar solvent; using different bead materials or sizes; using pump-probe techniques to detect superradiance. These experiments may assist in determining the underlying causes of second law violations and thus restore the conservation laws to their deserved prominence.

It seems intuitive that a knowledge of the microscopic properties of water (polar and covalent bonds, and clustering) is required to understand how a solvent's molecular motion can propel the colloidal particle for two seconds or more. However, the fluctuation theorem was not specifically designed to analyze this type of experiment and so "the many degrees of freedom associated with the solvent molecules are recast into the macroscopic material properties of viscosity and temperature". Thus the use of a theory based on Langevin dynamics has allowed many difficult questions concerning microscopic dynamics to be ignored. Nevertheless they are important and in particular it is necessary to state how solvent molecules can cause linear motion in a colloidal particle 12 magnitudes larger than their own yet at the same time conserve momentum. The most likely answer is that an undetected flow of energy obeying an exponential law has caused this effect.

Dissipative structures such as turbulence are well-known centers of entropy decrease. They form irreversibly in order to dissipate increasing energy flow, thereby allowing a greater flow than the simpler structures they replaced. They differ sharply from the reversible "entropy consumption" processes predicted by the fluctuation theorem which occur during constant flow. Because dissipative structures are reproducible and repeating they exhibit a spatial and temporal symmetry that suggests conformance with the conservation laws. On the other hand, entropy consumption processes possess neither of these symmetries nor can it be demonstrated that they obey the conservation laws. If a second entropy generating mechanism does exist in nature, then the underlying theory that supports it is not readily apparent.

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