Fluctuation-dissipation theorem for metastable systems

We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.     

Fluctuation-dissipation theorem for a class of stationary open systems

A generalized fluctuation-dissipation theorem is proved in the frame of a Liouville-space formalism for stationary open systems in contact with reservoirs, and in general far from thermal equilibrium. It is shown, however, that the wellknown case of thermal equilibrium is included in the result.     

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.     

Very high non-thermal equilibrium population of optical phonons in GaAs

Extremely high equivalent temperatures of optical phonons were obtained in GaAs without detectable increase in the lattice temperature. The improvement upon previous experiment was due to the use of a pulsed Nd:Yag laser which was doubled by the GaAs sample itself and absorbed in its bulk. The non-equilibrium LO-phonon population attained before crystal breakdown was ～ 27 times larger than the thermal equilibrium population at the room temperature (290K). The equivalent temperature observed for LO-phonons was ～3700K.     

Birkhoff系统的时间积分定理

研究Birkhoff系统的时间积分定理.建立Birkhoff系统的时间积分等式，由此等式导出系统的类功率方程，Pfaff-Birkhoff积分变分原理以及Pfaff-Birkhoff-d′Alembert微分变分原理. 关键词： Birkhoff系统 时间积分等式 类功率方程 变分原理     

Generalized Noether theorems and applications

We generalize the first and second Noether theorems (Noether identities) to a constrained system in phase space. As an example, the conservation law deriving from Lagrange's formalism cannot be obtained fromH _E via the generalized first Noether theorem (GFNT); Dirac's conjecture regarding secondary first-class constraints (SFCC) is invalid in this example. A preliminary application of the generalized Noether identities (GNI) to nonrelativistic charged particles in an electromagnetic field shows that on the constrained hypersurface in phase space one obtains electric charge conservation. This conservation law is valid whether Dirac's conjecture holds true or not.     

Hydrostatic equilibrium and Tsallis’ equilibrium for self-gravitating systems

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We discuss a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium for self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions. Tsallis’ equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.     

Partial virial theorems for atomic-molecular systems

New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T _jk 〉+〈 V _jk 〉=0, where 〈V _jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T _jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom ⁴He²⁺ e ^? e ^? and the helium muon-electron mesoatom ⁴He²⁺μ^? e ^? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.     

Partial hypervirial theorems for atomic-molecular systems

A family of partial hypervirial theorems for physical properties of pairs of particles in three-and four-particle atomic-molecular systems is considered. The partial hypervirial theorems generalize the partial virial theorems proposed earlier. The sum rule is formulated, according to which the expectation values of the derivatives with respect to the interparticle distances are related to the products of the charges of pairs of the particles. This rule is used to check the accuracy of the calculation of variational wave functions for the positronium ion e ^? e ^? e ⁺. It is shown that the sum rule is two orders of magnitude more sensitive to the inaccuracy of the calculation of the wave function than the partial virial theorems and is five or six orders of magnitude more sensitive to it than the conventional virial theorem.     

Evidence for non-thermal excitation of energy levels in active biological systems

The ratio R of the intensities of anti Stokes and Stokes Raman shift lines of 124 cm^-1 and of 118 cm^-1 of active E. coli B was measured. For an oscillating system in therm equilibrium R ≈ 0.55 is expected whereas we find R ≈ 1.0. This shows that this system is excited strongly above thermal excitation in agreement with a previous theoretical conjecture [2–5].     

Generalized Noether theorems in canonical formalism for field theories and their applications

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.     

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this nonequilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging.     

Generalized entropy production fluctuation theorems for quantum systems

Based on trajectory-dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In Case (iii), we build on the treatment carried out by H T Quan and H Dong [arXiv/cond-mat:0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems (FTs) retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These FTs are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator-valued measurements.