The controversial problem of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated by a piston whose mass is equal to the mass of the fluid particles we obtain a rigorous explicit stationary non-equilibrium solution of the Boltzmann equation. It is shown that at equal pressures on both sides of the piston, the temperature difference induces a non-zero average velocity, oriented toward the region of higher temperature. It thus turns out that despite the absence of macroscopic forces the asymmetry of fluctuations results in a systematic macroscopic motion. This remarkable effect is analogous to the dynamics of stochastic ratchets, where fluctuations conspire with spatial anisotropy to generate direct motion. However, a different mechanism is involved here. The relevance of the discovered motion to the adiabatic piston problem is discussed.Comment: 14 pages,1 figur

We consider a one-dimensional system consisting of two infinite ideal fluids, with equal pressures but different temperatures T1 and T2, separated by an adiabatic movable piston whose mass M is much larger than the mass m of the fluid particules. This is the infinite version of the controversial adiabatic piston problem. The stationary non-equilibrium solution of the Boltzmann equation for the velocity distribution of the piston is expressed in powers of the small parameter ǫ = m/M , and explicitly given up to order ǫ 2 . In particular it implies that although the pressures are equal on both sides of the piston, the temperature difference induces a non-zero average velocity of the piston in the direction of the higher temperature region. It thus shows that the asymmetry of the fluctuations induces a macroscopic motion despite the absence of any macroscopic force. This same conclusion was previously obtained for the non-physical situation where M = m.

The simplest statistical-mechanical model of crystalline formation ͑or alloy formation͒ that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions contain both second-order phase transitions and first-order phase transitions ͑that involve phase separation or segregation͒ which are likely to illustrate the precursor physics behind the static charge-stripe ordering in cuprate systems. In addition, we find that the spinodal-decomposition temperature satisfies an approximate scaling law. ͓S0163-1829͑99͒05527-7͔

The time evolution of the adiabatic piston problem and the consequences of its stochastic motion are investigated. The model is a one dimensional piston of mass M separating two ideal fluids made of point particles with mass m ≪ M . For infinite systems it is shown that the piston evolves very rapidly toward a stationary nonequilibrium state with non zero average velocity even if the pressures are equal but the temperatures different on both sides of the piston. For finite system it is shown that the evolution takes place in two stages: first the system evolves rather rapidly and adiabatically toward a metastable state where the pressures are equal but the temperatures different; then the evolution proceeds extremely slowly toward the equilibrium state where both the pressures and the temperatures are equal. Numerical simulations of the model are presented. The results of the microscopical approach, the thermodynamical equations and the simulations are shown to be qualitatively in good agreement.

Objective: To validate the prognostic value of preoperative levels of CYFRA 21-1, CEA and the corresponding tumor marker index (TMI) in patients with stage I non-small cell lung cancer (NSCLC). Methods: Two hundred forty stage I NSCLC patients (80 in pT1 and 160 in pT2; 100 squamous cell carcinomas, 91 adenocarcinomas, 32 large-cell carcinomas, 17 with other histologies; 171 males and 69 females) who had complete resection (R0) between 1986 and 2004 were included in the analysis. CYFRA 21-1 and CEA were measured using the Elecsys system (Roche) and AxSym-System (Abbott), respectively. Univariate analysis was performed using the Kaplan-Meier method to identify potential associations between survival and age, gender, CYFRA 21-1, CEA and TMI. Results: Overall 3- and 5-year survival rates were 74 and 64%, respectively. Male gender (p = 0.0009) and age >70 years (p = 0.0041) were associated with a worse prognosis; there were no differences between pT1 and pT2 nor between histological subtypes. Three-year survival was 72% for CYFRA 21-1 levels >3.3 ng/ml versus 75% for levels ≤3.3 ng/ml, 71% for CEA > 6.7 ng/ml versus 75% for CEA ≤6.7 ng/ml (both p values >0.05). Corresponding 5-year survival rates were near 64% both for patients with CYFRA 21-1 values above and below the cutoff (3.3 ng/ml), and 49 and 66% for patients with values above and below the CEA cutoff (6.7 ng/ml), respectively (both p values >0.05). Overall survival did not vary in the different TMI risk groups (p = 0.73). Conclusions: In this cohort of early-stage NSCLC patients, male gender and age >70 years were associated with a worse outcome, but elevated levels of CEA and CYFRA 21-1, and TMI risk were not.

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We present some exact results for the ground states of the Falicov-Kimball model outside the symmetry point. Three ion configurations have been considered: the chessboard configuration and the completely empty and the fully occupied configurations.Using a method based onTchebycheff-Markov inequalities, we determine domains in the plane of chemical potentials p, and p, "where these configurations are ground states.