 Indeed, the laws of thermodynamics are among the most universal ones of all laws of physics. Yet this subject can prove difficult to grasp. Many view thermodynamics as merely a collection of ad hoc recipes, or are confused by unfamiliar novel concepts, such as the entropy, which have little in common with the theories to which students have got accu Many view thermodynamics as merely a collection of ad hoc recipes, or are confused by unfamiliar novel concepts, such as the entropy, which have little in common with the theories to which students have got accustomed in other areas of physics.

This text provides a concise yet thorough introduction to the key concepts which underlie statistical physics and thermodynamics. It begins with a review of classical probability theory and quantum theory, as well as a careful discussion of the notions of information and entropy, prior to embarking on the development of statistical physics proper. The crucial steps leading from the microscopic to the macroscopic domain are rendered transparent. In particular, the laws of thermodynamics are shown to emerge as natural consequences of the statistical framework.

While the emphasis is on clarifying the basic concepts, the text also contains many applications and classroom-tested exercises, covering all major topics of a standard course on statistical physics and thermodynamics. The text is suited both for a one-semester course at the advanced undergraduate or beginning graduate level and as a self-contained tutorial guide for students in physics, chemistry, and engineering.

Keywords: statistical physics , thermodynamics , probability , quantum theory , information , entropy , laws of thermodynamics , macroscopic phenomena. Entropy is a measure of how much this process has progressed. The entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the maximum entropy production principle.

In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.

The third law of thermodynamics states: As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value. This law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions include "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".

An important concept in thermodynamics is the thermodynamic system , which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume.

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Exchanges of work , heat , or matter between the system and the surroundings take place across this boundary. In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation.

The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in ; it can be a body of steam or air in a steam engine , such as Sadi Carnot defined in ; it can be the body of a tropical cyclone , such as Kerry Emanuel theorized in in the field of atmospheric thermodynamics ; it could also be just one nuclide i. Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed.

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For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle.

Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:. As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium. Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium.

Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes.

When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state. The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables.

State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.

A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities.

## Statistical Physics & Thermodynamics | LCSM

Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc. There are two types of thermodynamic instruments , the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument.

For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in , asserts that it is possible to measure temperature.

## 545.630 - Thermodynamics and Statistical Mechanics

An idealized thermometer is a sample of an ideal gas at constant pressure. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system.

A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest. When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected.

The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle. The central concept of thermodynamics is that of energy , the ability to do work. By the First Law , the total energy of a system and its surroundings is conserved. Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter.

In mechanics , for example, energy transfer equals the product of the force applied to a body and the resulting displacement. Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system , the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:.

Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively. Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system.

Classical Statistical Chemical Quantum thermodynamics. Zeroth First Second Third. System properties. Note: Conjugate variables in italics. Work Heat. Material properties. Carnot's theorem Clausius theorem Fundamental relation Ideal gas law. Free energy Free entropy. History Culture. History General Entropy Gas laws. Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics.

Caloric theory Theory of heat. The object has a net momentum associated with the kinetic energy we are considering. The energy associated with the thermal energy of an object is incoherent ; that is, the molecules of the object are moving in all directions randomly. Although the molecules have kinetic energy and momentum, the net momentum of the object as a result of its thermal energy is zero. The study of how the macroscopic thermal behavior of objects arises from the motion of its molecules is called statistical mechanics. The flow and control of thermal energy are of considerable interest and importance to organisms, in part since the rates at which some of the critical chemical reactions of life take place depend on the temperature of the system.

### 1.2 Statistical versus Classical Thermodynamics

As a result, many organisms may spend a lot of the energy they harvest to regulate their temperatures. Understanding the thermal energy that is necessarily associated with chemical reaction chains such as photosynthesis, respiration, and the Krebs cycle is an important component of the energy balance of the reactions. But perhaps even more important for modern biology is understanding the statistical mechanics of biological systems.

The random motion of molecules plays a huge role in how the basic molecular mechanisms of biological systems take place, for example, the motion of uneven distributions of chemicals chemical gradients, Fick's law, etc. Our treatment of thermodynamics will therefore blend with a statistical mechanical description of the phenomena and an extended description of the role played by random molecular motions.

A word of warning: Thermodynamics and occasionally some elements of statistical mechanics is discussed in physics, chemistry, and biology classes. This might seem as if it would help, but in fact it often creates problems. The three fields each have their own "most important" aspects of these topics for their interests and they therefore may make different starting assumptions. Biologists often assume everything happens at constant pressures; chemists ignore coherent motions; physicists suppress chemical changes. While these may be perfectly reasonable assumptions for the examples they are each considering, often these assumptions are not highlighted.

The choice of which thermodynamic variables to use and how to express the laws may be different. This means that the "laws of thermodynamics" may look different in your different classes! Here, we will do our best to include all forms of energy — at least as a basis for discussion — and to be explicit about what we choose to ignore in our various discussions.

Thermodynamics is about the forms energy can take and how it is transferred from one form to another.