Estudamos um processo de transferência de calor entre um corpo de capacidade térmica C(T) e uma sequência de N reservatórios térmicos cujas temperaturas são uniformemente espaçadas entre a temperatura inicial T0 e a temperatura final T N. O corpo e os reservatórios térmicos são isolados do resto do universo e o corpo é colocado em contato térmico sucessivamente com reservatórios de temperatura crescente. Determinamos a variação de entropia do sistema termodinâmico composto no processo total, em que a temperatura do corpo varia de T0 a T N. Encontramos que para valores grandes de N a variação total de entropia é proporcional a (T N - T0) / N, mas eventualmente um comportamento não monotônico surge em valores pequenos de N.

We study a process of heat transfer between a body of heat capacity C(T) and a sequence of N heat reservoirs, with temperatures equally spaced between an initial temperature T0 and a final temperature T N. The body and the heat reservoirs are isolated from the rest of the universe, and the body is brought in thermal contact successively with reservoirs of increasing temperature. We determine the change of entropy of the composite thermodynamic system in the total process in which the temperature of the body changes from T0 to T N. We find that for large values of N the total change of entropy of the composite process is proportional to (T N - T0) / N, but eventually a non-monotonic behavior is found at small values of N.

Sandpile models with conserved number of particles (also called fixed energy sandpiles) may undergo phase transitions between active and absorbing states. We generalize the Manna sandpile model with fixed number of particles, introducing a parameter -1 < lambda < 1 related to the toppling of particles from active sites to its first neighbors. In particular, we discuss a model with height restrictions, allowing for at most two particles on a site. Sites with double occupancy are active, and their particles may be transfered to first neighbor sites, if the height restriction do allow the change. For lambda = 0 each one of the two particles is independently assigned to one of the two first neighbors and the original stochastic sandpile model is recovered. For lambda = 1 exactly one particle will be placed on each first neighbor and thus a deterministic (BTW) sandpile model is obtained. When lambda = -1 two particles are moved to one of the first neighbors, and this implies that the density of active sites is conserved in the evolution of the system, and no phase transition is observed. Through simulations of the stationary state, we estimate the critical density of particles and the critical exponents as functions of lambda.

A one dimensional non-equilibrium stochastic model is proposed where each site of the lattice is occupied by a particle, which may be of type A or B. The time evolution of the model occurs through three processes: autocatalytic generation of A and B particles and spontaneous conversion A -> B. The two-parameter phase diagram of the model is obtained in one- and two-site mean field approximations, as well as through numerical simulations and exact solution of finite systems extrapolated to the thermodynamic limit. A continuous line of transitions between an active and an absorbing phase is found. This critical line starts at a point where the model is equivalent to the contact process and ends at a point which corresponds to the voter model, where two absorbing states coexist. Thus, the critical line ends at a point where the transition is discontinuous. Estimates of critical exponents are obtained through the simulations and finite-size-scaling extrapolations, and the crossover between universality classes as the voter model transition is approached is studied.

Com frequência, cálculos das propriedades termodinâmicas em modelos mecânico-estatísticos envolvem problemas de contagem bastante complexos. Um caso deste tipo, que tem sido estudado há bastante tempo, é o do cálculo do número de maneiras de inscrever cadeias numa rede regular, respeitando o vínculo de volume excluído, isto é, cada sítio da rede pode ser ocupado por apenas um monômero. Em redes de dimensão finita e maior que um, o único caso deste problema que foi exatamento resolvido é o de dímeros (cadeias de dois monômeros que ocupam sítios contíguos) em uma rede bidimensional e no limite em que esta é completamente preenchida. Neste artigo, apresentamos a solução deste problema na rede unidimensional de duas maneiras diferentes. Em particular, resolvemos o problema utilizando a matriz de transferência, que pode ser aplicada também para tratar do caso bidimensional, levando a resultados bastante precisos. No final, obtemos e discutimos as equações de estado do gás de rede de cadeias.

Often calculations in statistical mechanics lead to rather complex counting problems. A problem of this type, which has been studied for a long time, is the determination of the number of ways to place chains on a regular lattice, respecting the excluded volume constraint, which states that each site of the lattice may be occupied by at most one monomer. In particular, one is interested in calculating this number in the thermodynamic limit, in which the lattice becomes infinite with the fraction of sites which are occupied by monomers kept constant. In lattices of dimension larger than one, the only particular case of this problem which was exactly solved is for dimers (chains with two monomers on first neighbor sites) in the limit of full lattice and for two-dimensional lattices. In this paper we present the solution of the problem on a one-dimensional lattice in two different ways. In particular, we solve the problem using a transfer matrix, which may also be applied in the two-dimensional case, leading to quite precise results. Finally, we obtain and discuss the state equations of the lattice gas formed by chains.

We study the thermodynamic properties of a semiexible polymer confined inside strips of widths L <= 9 defined on a square lattice. The polymer is modeled as a self-avoiding walk and a short-range interaction between the monomers and the walls is included through an energy <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">associated with each monomer placed on one of the walls. Also, an energy <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">b is associated with each elementary bend of the walk. The free energy of the model is obtained exactly through a transfer matrix formalism. The profile of monomer density and the force on the walls are obtained. We notice that as <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">b is decreased, the range of values of <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">which the density profi le is neither convex nor concave increases, and for sufficiently attracting walls (<IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif"> < 0) we find that in general the attractive force is maximum for <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">b < 0, that is, for situations where the bends are favored.

Self-avoiding chains on regular lattices are frequently used as models to study thermodynamic properties of linear polymers, particularly regarding critical phenomena which may occur in these systems. We review these models, concentrating on their properties under geometric constraints, when the walks are placed inside strips or pores. In these cases the models may be solved using a transfer matrix formalism for the generating functions. A short range interaction between the sites visited by the walks and the walls is included in the model and the distribution of the sites and the forces on the walls are studied as functions of the strength of this interaction.