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Lecture

Entropy and Disorder: Statistical Interpretation

In course

PHYS-106(h): General physics : thermodynamics

Le but du cours de Physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de prévoir quantitativement les conséquences de ces phénomène ...

Description

This lecture covers the statistical interpretation of entropy and disorder, focusing on calculating the multiplicity of micro-states in different configurations. Starting with the concept of irreversible adiabatic processes, the lecture delves into determining the number of micro-states in various scenarios. Through examples involving water bottles and books, the instructor explains the calculation of multiplicity and the significance of different configurations. The lecture progresses to discuss the general formula for multiplicity and the considerations for avoiding double counting. By exploring the distribution of particles and the selection of objects, the lecture illustrates how to calculate the total number of possibilities and determine the most probable configurations.

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Instructor

Ivo Furno

Official source

Ontological neighbourhood

Physics

Thermodynamics: Statistical mechanics

Related concepts (28)

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Irreversible process

In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics. All complex natural processes are irreversible, although a phase transition at the coexistence temperature (e.g. melting of ice cubes in water) is well approximated as reversible. In thermodynamics, a change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy.

Probability interpretations

The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities.

Frequentist probability

Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in many trials (the long-run probability). Probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). The continued use of frequentist methods in scientific inference, however, has been called into question. The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the classical interpretation.

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

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