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Register a new userThermodynamics of static: Observers in Gibbs paradox
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In this work, Gibbs paradox was discussed from the view of observer. The limitations of real observer are analyzed quantitatively. The entropy of mixing was found to be determined by both the identification ability and the information already in hand of an observer.
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This paper introduces the basic concepts of information theory. Based on these concepts, we regard the states in the state space and the types of ideal gases as the symbols in a symbol set to calculate the mixing entropy of ideal gas involved in Gibbs Paradox. The discussion above reveals that the non-need for distinguishing can resolve the contradiction of Gibbs Paradox, implying the introduction of indistinguishability is not necessary. Further analysis shows that the information entropy of gas molecular types does not directly correlate to the energy of a gas system, so it should not be used for calculating thermodynamic and statistical dynamic entropies. Therefore, the mixing entropy of the ideal gas is independent of the molecular types and is much smaller than the value commonly thought.
The classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an ignorant observer, who cannot distinguish the gases, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical statistical mechanics. This demonstrates the importance of accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.
We study the propagation of entanglement after quantum quenches in the non-integrable para-magnetic quantum Ising spin chain. Tuning the parameters of the system, we observe a sudden increase in the entanglement production rate, which we show to be related to the appearance of new quasi-particle excitations in the post-quench spectrum. We argue that the phenomenon is the non-equilibrium version of the well-known Gibbs paradox related to mixing entropy and demonstrate that its characteristics fit the expectations derived from the quantum resolution of the paradox in systems with a non-trivial quasi-particle spectrum.
Reciprocity is a fundamental principle governing various physical systems, which ensures that the transfer function between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity have been mostly considered in dynamic systems, for electromagnetic, acoustic and mechanical wave propagation associated with spatio-temporal variations. Here we show that it is possible to strongly break reciprocity in static systems, realizing mechanical metamaterials that, by combining large nonlinearities with suitable geometrical asymmetries, and possibly topological features, exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. In addition to extending non-reciprocity and isolation to statics, our work sheds new light on the understanding of energy propagation in non-linear materials with asymmetric crystalline structures and topological properties, opening avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.
Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically, on the energy-momentum tensor. We discuss a few examples, which illustrate the dynamical aspect of the length-contraction effect within the framework of Special Relativity. We show some pitfalls associated with direct application of the length contraction formula in cases when an extended object is accelerated. Our analysis reveals intimate connections between length contraction and the dynamics of internal forces within the accelerated system. The developed approach is used to analyze the correlation between two congruent disks - one stationary and one rotating (the Ehrenfest paradox). Specifically, we consider the transition of a disk from the state of rest to a spinning state under the applied forces. It reveals the underlying physical mechanism in the corresponding transition from Euclidean geometry of stationary disk to Lobachevskys (hyperbolic) geometry of the spinning disk in the process of its rotational boost. A conclusion is made that the rest mass of a spinning disk or ring of a fixed radius must contain an additional term representing the potential energy of non-Euclidean circumferential deformation of its material. Possible experimentally observable manifestations of Lobachevskys geometry of rotating systems are discussed.
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