Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation

We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated $N$-particle system, the microcanonical TDFs exhibit (N-1) singular (non-analytic) microscopic phase transitions of the formal order N/2, separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text, references adde

Adiabatic invariance with first integrals of motion

The construction of a microthermodynamic formalism for isolated systems based on the concept of adiabatic invariance is an old but seldom appreciated effort in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33, 225 (1910)]. An apparently independent extension of such formalism for systems bearing additional first integrals of motion was recently proposed by Hans H. Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic invariance even in such singular cases. After some remarks in connection with the formalism pioneered by Hertz, it will be suggested that such an extension can incidentally explain the success of a dynamical method for computing the entropy of classical interacting fluids, at least in some potential applications where the presence of additional first integrals cannot be ignored.Comment: 2 pages, no figures (REVTeX 4

Response variability in balanced cortical networks

We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean-field description in which synaptic currents can be treated as Gaussian noise, the mean and autocorrelation function of which are calculated self-consistently from the firing statistics of single model neurons. Within this description, we find that the irregularity of spike trains is controlled mainly by the strength of the synapses relative to the difference between the firing threshold and the post-firing reset level of the membrane potential. For moderately strong synapses we find spike statistics very similar to those observed in primary visual cortex.Comment: 22 pages, 7 figures, submitted to Neural Computatio

Condensation temperature of interacting Bose gases with and without disorder

The momentum-shell renormalization group (RG) is used to study the condensation of interacting Bose gases without and with disorder. First of all, for the homogeneous disorder-free Bose gas the interaction-induced shifts in the critical temperature and chemical potential are determined up to second order in the scattering length. The approach does not make use of dimensional reduction and is thus independent of previous derivations. Secondly, the RG is used together with the replica method to study the interacting Bose gas with delta-correlated disorder. The flow equations are derived and found to reduce, in the high-temperature limit, to the RG equations of the classical Landau-Ginzburg model with random-exchange defects. The random fixed point is used to calculate the condensation temperature under the combined influence of particle interactions and disorder.Comment: 7 pages, 2 figure

On the work distribution for the adiabatic compression of a dilute classical gas

We consider the adiabatic and quasi-static compression of a dilute classical gas, confined in a piston and initially equilibrated with a heat bath. We find that the work performed during this process is described statistically by a gamma distribution. We use this result to show that the model satisfies the non-equilibrium work and fluctuation theorems, but not the flucutation-dissipation relation. We discuss the rare but dominant realizations that contribute most to the exponential average of the work, and relate our results to potentially universal work distributions.Comment: 4 page

p>2 spin glasses with first order ferromagnetic transitions

We consider an infinite-range spherical p-spin glass model with an additional r-spin ferromagnetic interaction, both statically using a replica analysis and dynamically via a generating functional method. For r>2 we find that there are first order transitions to ferromagnetic phases. For r<p there are two ferromagnetic phases, one non-glassy replica symmetric and one exhibiting glassy one-step replica symmetry breaking and aging, whereas for r>=p only the replica symmetric phase exists.Comment: AMSLaTeX, 13 pages, 23 EPS figures ; one figure correcte