macroscopic perspective, in classical thermodynamics the entropy is interpreted as a state function of a thermodynamic system: that is, a property depending Entropy is a thermodynamic state variable that quantifies the probabilistic distribution of accessible microstates in a system. The term and the concept are used in diverse fields, from classical thermodynamics (where it was first recognized), to the microscopic description of nature in statistical physics, and the principles of information theory. It has far-ranging applications in chemistry and The entropy of a system depends on its internal energy and its external parameters, such as its volume. In the thermodynamic limit, this fact leads to an equation relating the change in the internal energy U {\textstyle U} to changes in the entropy and the external parameters. This relation is known as the fundamental thermodynamic relation. If external pressure p {\textstyle p} bears on the volume V {\textstyle V} as the only external parameter, this relation is: d U = T d S − p d V {\displaystyle \mathrm {d} U=T\ \mathrm {d} S-p\ \mathrm…

The Mathematical Structure of the Second Law of Thermodynamics The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose increase characterizes the possible state changes under adiabatic conditions. It is one of the few really fundamental physical laws (in the sense that no deviation, however tiny, is permitted) and its consequences are far reaching. This principle is independent of models, statistical mechanical or otherwise, and can be understood without recourse to Carnot cycles, ideal gases and other assumptions about such things as `heat', `temperature', `reversible processes', etc., as is usually done. Also the well known formula of statistical mechanics, S = -\sum p log p, is not needed for the derivation of the entropy principle. This contribution is partly a summary of our joint work (Physics Reports, Vol. 310, 1--96 (1999)) where the existence and uniqueness of S is proved to be a consequence of certain basic properties of the relation of adiabatic accessibility among equilibrium states.

Microcanonical Ensemble Extensive Thermodynamics of Tsallis Statistics The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution functions are derived by the thermodynamic method based upon the use of the fundamental equation of thermodynamics and the statistical definition of the functions of the state of the system. It is shown that if the entropic index $\xi=1/(q-1)$ in the microcanonical ensemble is an extensive variable of the state of the system, then in the thermodynamic limit $\tilde{z}=1/(q-1)N=const$ the principle of additivity and the zero law of thermodynamics are satisfied. In particular, the Tsallis entropy of the system is extensive and the temperature is intensive. Thus, the Tsallis statistics completely satisfies all the postulates of the equilibrium thermodynamics. Moreover, evaluation of the thermodynamic identities in the microcanonical ensemble is provided by the Euler theorem.

In thermodynamics, it is essential to distinguish between state functions and process functions. The reason is that the simple compressible thermodynamic system is a bivariate-process system, and the change of internal energy, a state function, corresponds to two process functions, heat and work. Among the state functions in thermodynamics, entropy is a special one because it has to be defined through a process function, exchanged heat δ Q , and a unique factor of integration, 1/T. In heat transfer, it is shown that Fourier's law and the differential equation of heat conduction are both relations of state quantities alone, and process quantities appear when an integration with respect to time is applied. Moreover, an incompressible heat conduction medium element without conversion between heat and work is a univariate-process system governed by a single variable, temperature. In this case, the change of the thermal energy ("heat content") stored in the system, a state quantity as a function of T alone, corresponds to only one process quantity, the transferred heat. Therefore, on the one hand, it is unnecessary to strictly distinguish between state quantities and process quantities in heat transfer, and on the other hand, there is no need to use a factor of integration to prove entransy a state quantity in heat transfer. Thermodynamics and heat transfer are two parallel sub-disciplines in thermal science. It is incorrect to deny entransy as a state quantity in heat transfer by

In classical thermodynamics, entropy (from Greek τρoπή (tropḗ) 'transformation') is a property of a thermodynamic system that expresses the direction In classical thermodynamics, entropy (from Greek τρoπή (tropḗ) 'transformation') is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-19th century to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Ent In classical thermodynamics, the entropy of the reference state can be put equal to zero at any convenient temperature and pressure. For example, for pure substances, one can take the entropy of the solid at the melting point at 1 bar equal to zero. From a more fundamental point of view, the third law of thermodynamics suggests that there is a preference to take S = 0 at T = 0 (absolute zero) for perfectly ordered materials such as crystals. S(P, T) is determined by followed a specific path in the P-T diagram: integration over T at constant pressure P0, so that dP = 0, and in the second integral one integrates over P at constant temperature T, so that dT = 0. As the entropy is a function of state the result is independent of the path. The above relation shows that the determination of the entropy requires knowledge of the heat capacity and the equation of state (which is the relation between P,V, and T of the substance involved). Normally these are complicated functions and numerical integration is needed. In simple cases it is possible to get analytical expressions for the entropy. In the case of an ideal gas, the heat capacity is constant and the ideal gas law PV = nRT gives that αVV = V/T = nR/p, with n the number of moles and R the molar ideal-gas constant. So, the molar entropy of an ideal gas is given by

exists as regards the great number of uncoordinated elements required. Just as the entropy of a body is defined as a function of the macroscopic state , only