# Thermodynamics and statistical mechanics pdf

Thermodynamics and Statistical Mechanics. Richard Fitzpatrick. Professor of Physics. The University of Texas at Austin. Contents. 1 Introduction. 7. Intended. An Introduction to Thermodynamics and Statistical. Mechanics, Second Edition. This introductory textbook for standard undergraduate courses in. Lecture Notes on Thermodynamics and Statistical Mechanics. (A Work in Progress). Daniel Arovas. Department of Physics. University of California, San Diego.

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## Thermodynamics and statistical mechanics

The statistical ensemble is a probability distribution over all possible states of the system. In classical statistical mechanics, the ensemble is a probability distribution over phase points as opposed to a single phase point in ordinary mechanics , usually represented as a distribution in a phase space with canonical coordinates. In quantum statistical mechanics, the ensemble is a probability distribution over pure states, [note 2] and can be compactly summarized as a density matrix.

As is usual for probabilities, the ensemble can be interpreted in different ways:  an ensemble can be taken to represent the various possible states that a single system could be in epistemic probability , a form of knowledge , or the members of the ensemble can be understood as the states of the systems in experiments repeated on independent systems which have been prepared in a similar but imperfectly controlled manner empirical probability , in the limit of an infinite number of trials.

These two meanings are equivalent for many purposes, and will be used interchangeably in this article.

However the probability is interpreted, each state in the ensemble evolves over time according to the equation of motion. Thus, the ensemble itself the probability distribution over states also evolves, as the virtual systems in the ensemble continually leave one state and enter another. The ensemble evolution is given by the Liouville equation classical mechanics or the von Neumann equation quantum mechanics.

These equations are simply derived by the application of the mechanical equation of motion separately to each virtual system contained in the ensemble, with the probability of the virtual system being conserved over time as it evolves from state to state. One special class of ensemble is those ensembles that do not evolve over time.

These ensembles are known as equilibrium ensembles and their condition is known as statistical equilibrium. Statistical equilibrium occurs if, for each state in the ensemble, the ensemble also contains all of its future and past states with probabilities equal to the probability of being in that state.

Statistical thermodynamics[ edit ] The primary goal of statistical thermodynamics also known as equilibrium statistical mechanics is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them.

## Modern Thermodynamics with Statistical Mechanics

In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium , and the microscopic behaviours and motions occurring inside the material.

Whereas statistical mechanics proper involves dynamics, here the attention is focussed on statistical equilibrium steady state.

NaN03 time Figure 4. The examples c and d show that reactions can spontaneously occur even if they are disfavoured in terms of the enthalpy changes. What then is the driving force? It is clear from these examples that in some way each system is spontaneously moving towards a more disordered or more The Second and Third Laws: Entropy uniform state. It is also the case although perhaps less obvious that the systems have lost some capacity for carrying out work for example, the expanding gas could have been used to do work on a turbine.

We could even have found examples where the system apparently spontaneously becomes more ordered, such as the crystallization of a supersaturated solution. The driving force is that in each case of a spontuneozis process the total entropy of the system plus its surroundings has increased: where A S is the change in entropy upon the process occurring. The total entropy spontaneously tends to increase until equilibrium is attained, and then stays constant see Box 4. When heat flows into the 27 28 Thermodynamics and Statistical Mechanics surroundings, it leads to an increase in their disorder. Furthermore, the amount of disorder caused is greater for a given heat flow, the lower the temperature of the surroundings.