Abstract This paper considers an Ostwald ripening process in which new droplets are injected at a constant rate, with a fixed distribution of radii, and in which droplets are removed when they grow to a specified maximum radius. This process exhibits a transition from a steady state to a limit cycle as a parameter is varied. The instability is shown to be related to the roots of the Laplace transform of a response kernel. A model is described which gives a good approximation of the period of the limit cycle. The system may also exhibit chaotic behaviour. The relevance of the model to atmospheric precipitation is discussed.
Abstract There is evidence that taking the time average of the work performed by a thermally isolated system effectively ‘transforms’ the adiabatic process into an isothermal one. This approach allows inherent quantities of adiabatic processes to be accessed through the definitions of isothermal processes. A fluctuation theorem is then established, linking the time-averaged work to the quasistatic work. Numerical evidence supporting this equality is provided for a classical harmonic oscillator with a driven linear equilibrium position parameter. Furthermore, the strong inequality for the average work is derived from the deduced fluctuation theorem using optimality arguments.
Abstract We investigate simplicial complexes deterministically growing from a single vertex. In the first step, a vertex and an edge connecting it to the primordial vertex are added. The resulting simplicial complex has a 1-dimensional simplex and two 0-dimensional faces (the vertices). The process continues recursively: On the n -th step, every existing d − dimensional simplex ( d ⩽ n − 1 ) joins a new vertex forming a ( d + 1 ) − dimensional simplex; all 2 d + 1 − 2 new faces are also added so that the resulting object remains a simplicial complex. The emerging simplicial complex has intriguing local and global characteristics. The number of simplices grows faster than n ! , and the upper-degree distributions follow a power law. Here, the upper degree (or d -degree) of a d -simplex refers to the number of ( d + 1 ) -simplices that share it as a face. Interestingly, the d -degree distributions evolve quite differently for different values of d . We compute the Hodge Laplacian spectra of simplicial complexes and show that the spectral and Hausdorff dimensions are infinite. We also explore a constrained version where the dimension of the added simplices is fixed to a finite value m . In the constrained model, the number of simplices grows exponentially. In particular, for m = 1, the spectral dimension is 2. For m = 2, the spectral dimension is finite, and the degree distribution follows a power law, while the 1-degree distribution decays exponentially.
Abstract Landauer’s principle states that erasing a bit of information at fixed temperature T costs at least k B T ln 2 units of work. Here we investigate erasure at varying temperature, to which Landauer’s result does not apply. We formulate bit erasure as a stochastic nonequilibrium process involving a compression of configuration space, with physical and logical states associated in a symmetric way. Erasure starts and ends at temperature T, but temperature can otherwise vary with time in an arbitrary way. Defined in this way, erasure is governed by a set of nonequilibrium fluctuation relations that show that varying-temperature erasure can done with less work than k B T ln 2 . As a result, erasure and the complementary process of bit randomization can be combined to form a work-producing engine cycle.
Abstract Recent experiments show striking unexpected features when alternating square magnetic field pulses are applied to ferromagnetic samples: domains show area reduction and domains walls change their roughness. We explain these phenomena with a simple scalar-field model, using a numerical protocol that mimics the experimental one. For a bubble and a stripe domain, we reproduce the experimental findings: the domains shrink by a combination of linear and exponential behavior. We also reproduce the roughness exponents found in the experiments. Our results suggest that the observed effects are due to a change in the disorder correlation length when the domain walls are subject to alternating fields during the first cycles, where the initial state of the interface plays a crucial role. Finally, our simulations explain the area loss by the interplay between disorder effects and effective fields induced by the local domain curvature.
Abstract The thermodynamical properties of the photon-plasma system have been studied using statistical physics approach. Photons develop an effective mass in the medium thus—as a result of the finite chemical potential—a photon Bose–Einstein condensation can be achieved by adjusting one of the relevant parameters (temperature, photon density and plasma density) to criticality. Due to the presence of the plasma, Planck’s law of blackbody radiation is also modified with the appearance of a gap below the plasma frequency where a condensation peak of coherent radiation arises for the critical system. This is in accordance with recent optical microcavity experiments which are aiming to develop such photon condensate based coherent light sources. The present study is also expected to have applications in other fields of physics such as astronomy and plasma physics.
Abstract Computing of partition function is the most important statistical inference task arising in applications of graphical models (GM). Since it is computationally intractable, approximate methods have been used in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular and successful approaches of a variational type. In this paper, we propose two new variational schemes, coined Gauged-MF (G-MF) and Gauged-BP (G-BP), improving MF and BP, respectively. Both provide lower bounds for the partition function by utilizing the so-called gauge transformation which modifies factors of GM while keeping the partition function invariant. Moreover, we prove that both G-MF and G-BP are exact for GMs with a single loop of a special structure, even though the bare MF and BP perform badly in this case. Our extensive experiments indeed confirm that the proposed algorithms outperform and generalize MF and BP.