Definition Of Thermodynamic Entropy Research Articles

Inferring entropy from structure.

The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively inefficient to sample or difficult to obtain experimentally. It is beneficial, therefore, to relate the entropy to other integrated properties which are accessible out of equilibrium. We focus on the structure factor, which describes the spatial correlations of density fluctuations and can be directly measured by scattering. The information gained by a given structure factor regarding an otherwise unknown system provides an upper bound for the system's entropy. We find that the maximum-entropy model corresponds to an equilibrium system with an effective pair interaction. Approximate closed-form relations for the effective pair potential and the resulting entropy in terms of the structure factor are obtained. As examples, the relations are used to estimate the entropy of an exactly solvable model and two simulated systems out of equilibrium. The focus is on low-dimensional examples, where our method, as well as a recently proposed compression-based one, can be tested against a rigorous direct-sampling technique. The entropy inferred from the structure factor is found to be consistent with the other methods, superior for larger system sizes, and accurate in identifying global transitions. Our approach allows for extensions of the theory to more complex systems and to higher-order correlations.

Exactness of measured/predicted temperature distributions for heat generation in arbitrary non-variable cross-section bar using entropy generation method

• A novel application of second law of thermodynamics. • Usable for validation purposes in every study which involves heat transfer. • Presenting a unique value of non-dimensional total entropy generation rate. • Investigating the effect of cross sectional geometry on lost work. The purpose of the present study is to introduce the entropy generation method as a new validation tool of numerical and experimental studies in the heat transfer field where there exist no similar solutions with which to compare results. Analysis of temperature profiles has been conducted in bars with internal thermal energy generation, constant temperature boundary condition and arbitrary non-variable cross section. The bars have steady state Fourier heat conduction and uniform thermal energy generation. The total rate of entropy generation can be calculated using two different methods: The 1st method is based on integrating local entropy generation rate on the solution domain, and the 2nd one is based on the thermodynamic definition of entropy and the Clausius theorem. The equality of these two results depends on the exactness of the applied temperature profile. The closer the entropy generation rates in the control volume (EGRCVs), the more accurate the predicted temperature profile would be and thus, the obtained results are more reliable. Seven different geometries have been examined for the bar cross section and a correlation between error of temperature distribution and error of entropy generation has been obtained. Moreover, the effect of the cross section geometry on entropy generation has been studied and the distribution of local entropy generation rate for the selected geometries was plotted.

Simulation study of entropy production in the one-dimensional Vlasov system

The coarse-grain averaged distribution function of the one-dimensional Vlasov system is obtained by numerical simulation. The entropy productions in cases of the random field, the linear Landau damping, and the bump-on-tail instability are computed with the coarse-grain averaged distribution function. The computed entropy production is converged with increasing length of coarse-grain average. When the distribution function differs slightly from a Maxwellian distribution, the converged value agrees with the result computed by using the definition of thermodynamic entropy. The length of the coarse-grain average to compute the coarse-grain averaged distribution function is discussed.

On the laws of thermodynamics from the escort average and on the uniqueness of statistical factors

We consider the relation between the statistical weight and the laws of thermodynamics. Our path bases on the infinitesimal perturbation from outside of the thermodynamical system. It is fair to say that the form of the first laws of thermodynamics and the Clausius' definition of thermodynamic entropy are commensurately altered once we employ the escort average of statistical weight but preserves the forms in the limit of the usual weight. We also see an example for the unique determination of the statistical factor (so-called the Gibbs theorem) in addition to the Boltzmann and the Tsallis ones.

On the thermodynamics of the oceanic general circulation: entropy increase rate of an open dissipative system and its surroundings

The role of thermodynamics in the oceanic general circulation is investigated. The ocean isregarded as an open dissipative system that exchanges heat and salt with the surroundingsystem. A new quantitative method is presented to express the rate of entropy increase for alarge-scale open system and its surroundings by the transports of heat and matter. This methodis based on Clausius’s definition of thermodynamic entropy, and is independent of explicitexpressions of small-scale dissipation processes. This method is applied to an oceanic generalcirculation model, and the entropy increase rate is calculated during the spin-up period of themodel. It is found that, in a steady-state, the entropy increase rate of the ocean system is zero, whereas that of the surroundings shows positive values, for both heat and salt transports. Thezero entropy increase rate of the ocean system represents the fact that the system is in a steadystate, while the positive entropy increase rate in the surroundings is caused by irreversibletransports of heat and salt through the steady-state circulation. The calculated entropy increaserate in the surroundings is 1.9×1011WK-1, and is primarily due to the heat transport. It issuggested that the existence of a steady-state dissipative system on the Earth, from a livingsystem to the oceanic circulation, has a certain contribution to the entropy increase in itsnonequilibrium surroundings.