Phase space, Microstates and Macrostates ,Ensemble, Constraints
This note provides us an information about Phase space, Microstates and Macrostates ,Ensemble,and Constraints
Summary
This note provides us an information about Phase space, Microstates and Macrostates ,Ensemble,and Constraints
Things to Remember
- The specification of a molecule in a cell is called microstate.
- The random collection of identical and independent assemblies is called ensemble.
- The condition imposed in the selection of systems, ensemble etc are called constraints.
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Subjective Questions
Q1:
Define GAS.
Type: Short Difficulty: Easy
<p>General adaptation syndrome, or GAS, is a term used to describe the body’s short- term and long-term reaction to stress.</p>
<p>The general body response arguments the bodily functions that protect the organism from injury, psychological and physical and suppress those functions non-essential to life. The general adaptation syndrome has three stage : alarm stage, resistance stage, and exhaustion stage. </p>
Q2:
Explain the stages of GAS.
Type: Long Difficulty: Easy
<p><strong>-Alarm reaction:</strong></p>
<p>When a person is first confronted with a <strong>stressor</strong>, something that brings about stress, they enter the first phase of the GAS. This first phase is known as the <strong>Alarm Phase</strong>.</p>
<p>During this immediate and involuntary phase, a hormone called epinephrine, also known as adrenaline, is released among plenty of other biochemical messengers.</p>
<p>These biochemicals cause lots of changes, including:</p>
<ul>
<li>An increase of blood sugar, a.k.a. blood glucose. You know that drinking tons of sugar-laced soft drinks give you an energy rush. Your body tries to mimic this naturally by quickly releasing lots of sugar into the bloodstream from its energy stores. This energy supply is necessary during times of stress so you stay mentally alert and are ready to move, run, or fight at a moment's notice.</li>
<li>An increase in blood pressure, heart rate, and respiratory rate so you get lots of oxygen and blood delivered to your important organs and muscles - muscles like skeletal muscles, the muscles that help you run, like your quads, and fight, like your triceps.</li>
<li>A concurrent decrease in blood flow to the skin and digestive organs because they're irrelevant in a fight or flight response, such as that found during the alarm stage. The last thing your body wants to do when under duress is give precious resources, like the blood that's filled with oxygen and sugar, to organs that will not help you immediately fight off a stressor or flee from it. What are you going to do, eat a picnic and digest some food while a bear is charging at you? I don't think so! And neither does your body.</li>
</ul>
<p>Psychologically speaking, a person may also experience fear, anger, anxiety, panic, and restlessness during the alarm phase.</p>
<p> </p>
<p>-Stage of resistance:</p>
<p>The alarm phase is many times enough to help us overcome something that stressed us out in the first place. But if the stressor goes on for several hours or more, we enter the <strong>Resistance Phase</strong>, the second phase of the GAS.</p>
<p>Staying in the high-strung alarm phase for too long is not conducive to the proper and optimal health and function of our body. Therefore, people in the resistance stage try to calm themselves down, deny the problem, shut down their emotions, and isolate themselves - all of this, in order to re-establish a sense of normality.</p>
<p>A person's physiological self also undergoes some important modifications at this time. During the resistance phase:</p>
<ul>
<li>Glucocorticoids, which are steroid hormones, as well as other biochemicals, begin to play an important role. They cause things like the breakdown of fat so that this fat can be used as a source of energy during long periods of stress.</li>
<li>These biochemicals also elevate and stabilize the levels of blood sugar, particularly in order to power the nervous system.</li>
</ul>
<p>As long as fat stores remain in enough quantity, the resistance phase can continue for weeks or even months and helps explains why people can survive a huge stressor, like starvation, for quite some time.</p>
<p>Of course, the preponderance of glucocorticoids doesn't come without a cost. Too many of these stress hormones over a long period of time delays wound healing and make a person more likely to get sick.</p>
<p> </p>
<p><strong>-Stage of exhaustion:</strong></p>
<p>It occurs when the person is unable to continue to adapt to internal and external environmental demands. Since the organism has depleted much of its reserve, one feels exhausted, he has no strength to deal with the stressor anymore the body can no longer compensate for or correct homeostatic balance if the stressor is too strong or continue.</p>
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Phase space, Microstates and Macrostates ,Ensemble, Constraints
Phase space
For the exact location of a molecule in three dimension space, the coordinate system is insufficient because the three-dimensional system is unable to give information about physical observable(e.g. velocity, energy, etc). So, to have the complete information about physical observables, velocity coordinates, in addition, is required. More generally, three position coordinates (x,y,z) and three momentum coordinates (px, py, pz) constitute a separate space known as phase space.
In short, Six-dimensional spaces of which three are position coordinates and three are momentum components is called phase space.
Phase space where the specification of a molecule is possible is called \(\mu \)-phase space.
6N dimensional space where we specify coordinates and momentum of N-molecules are called \(\gamma \)-phase space or \(\tau \)-phase space.
Volume of Phase space:
The elementary volume of phase space is called the cell.
If we consider a molecule then to specify it, we require three co-ordinates say dx, dy and dz and three momenta dpx, dpy and DPS.
then the volume=dx.dy.dz.dpx.dpy.dpz
From Heisenberg's uncertainty principle, we know that co-ordinates and momentum of a molecule can not be determined precisely at a time simultaneously. The value of uncertainty in position and momentum is of the order of Planck's constant dx.dpx\(\geq \) h, where h is Planck's constant.
Similarly,dy.dpy\(\geq \) h,dz.dpz\(\geq \) h.
\(\therefore \) volume = \(h^3\).
Microstates and Macrostates
The specification of a molecule in a cell is called microstate. The individual if remain always in the same region of the cell there is no change in microstate. If there is the exchange of molecules among the phase cells there is no change in microstate. If there is the exchange of molecules among the phase cells there will be the change in microstate.
Specification of a number of molecules in a cell is called macrostate. If a number of molecules always remain same in the confined region of phase space(cell) whichever may be the molecule, the macrostate remains same. If the initial number of molecules in the cell is not same with a final number of molecules, there will be macrostate.
Let us design three phase i.e.,three cells A, B, and C carrying molecules (a,b,c),(p,q) and f respectively. Molecules a,b and c if they are specified in cell A is called microstate of the cell. There are three molecules in A is the macrostate of the cell A.
| a,b,c | a,b,q | a,q |
| p,q | p,c | b,c,q |
| f | f | f |
Similarly, the specification of molecule p in cell B and f in cell C are their respective microstates. The total number of molecules in cell B is two and C is one refers to macrostate of cell B and C respectively.
If we exchange the molecules in cell A and B in such a way that the total number of molecules before and after exchange remains the same, there will be the change in microstate but no change in macrostate. On another hand, if there is the difference in a total number of molecules in cell A and B before and after the exchange, there will be a change in both microstates as well as macrostate.
Ensemble
Each gas molecule constitutes a system. The collection of gas molecules forms an assembly. The random collection of identical and independent assemblies is called ensemble. There are three types of ensemble.
(i) Microcanonical ensemble
(ii) Canonical ensemble
(iii) Grand canonical ensemble
Constraints
The condition imposed in the selection of systems, ensemble etc are called constraints. In other words, the restrictions employed in the selection of parameters is called constraints. For example, movement of balls in unidimensional abacus in the constraint in the movement of the ball. No, any ball can move in other possible directions.
Accessible states are the states consistent with the given constraints of the system.
Lesson
Classical Statistical Physics
Subject
Physics
Grade
Bachelor of Science
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