Events in Time

Basic Thermodynamics ~ J. Pohl ©

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Time, a grand abstract, is not a property of any system. Time is easily made quantitative on a relative scale. We think of the timekeeper as a "clock." By creating and counting its sequences of periodic events, a clock can be used to establish what happened first, second, thereafter and so on. Time does not participate in events, it is an observer. Some aspects of time with relation to system times and events are:

Batch Event: Some physical events exhibit the distinct aspects of time we call, a "start" and then later, an "end" (or "finish"). For want of a better term, thermodynamics calls such events, batch (or "increment" type>

To split a log with an ax, uncap a bottle or cook an egg, are examples. The "batch event" initiates with a distinct beginning... when the ax impacts the log, when the cap pops off, or when an egg is cracked on the edge of the pan. The batch event ends distinctly. In these cases it ends when the log becomes two falling pieces, when the cap pops free of the bottle, or when the egg is poured from its shell into the pan.

Systems events of a "batch" or "increment" type generally have some physical characteristic or mechanism, some manner of "catalyst or trigger," which upon actuation, initiates the event and another, later, which "stops" upon its completion.

Commonly, the initial state and its system properties are associated with the time of event commencement, designated with the subscript, "1." All system properties at the final time, the time at which the task is completed, are designated with the subscript, "2." System property differences , pressure for example are written, p₂ - p₁ or Δp. Work and heat do not exist; they are energy transfers. For a batch event they are written as W_1-2 or Q_1-2.

Continuing Event: Since time continues, all of physical reality experiences a continuing event. More pointedly, a system that receives energy steadily while energy in an equal amount passes from it (that is, having no system energy change) experiences a continuing event.

Null Event: The simplest event is a non-event, meaning no change. "Permanence" or the term "null event" is used by some. Concrete and steel structures of hydro-electric dams and bridges were designed with the intention of no change ever, to last forever. Our spent nuclear fuels (in their trash containers) will change negligibly, will be lethal to us for a few million years. Everything changes, of course. Time itself means change. Time has no meaning for the null event or the permanent system. Of course there is no permanance; physically that would amount to a denial of the reality - time.

Differential Event: Calculus is important to the development of science and thermodynamics. The differential event is an invention of Newton. This is the very special change of a system in the limit (with vanishing time) as to be so small as to be no change but yet a change. The notation "d" when written before a variable (e.g., dX) means the very slightest change of X, or the last of diminishing changes of X, before the change is zero, meaning no change.

Time and Time-Related Notations Time is a dimension; a human perception. Time can be quantified. Our clocks measure the lengths of our lives - as we live. Our clocks tell us where we are in the day, calenders place the day in a larger time frame - the year. We use the idea of time scientifically, to explain the past or predict the future. Some special definitions and notations for thermodynamics follow:

Time ~ "t " Time an abstract idea. We sense that it proceeds, we see changes in time of solar and lunar phenomena and of our own aging. The symbol, "t," is used to mean time in the arbitrary sense. Although we don't know when time began we have invented "clocks" that tell inform us time increments. The letter, "t," is a variable and is sometimes written beside an axis designating time.
Epoch, Era, Period or Event: In our studies it is useful to identify lengths of time the moments (years, hours or nanoseconds) of which have some commonality. An era, period or event is assumed to have an initiation, a beginning time, a duration, and an ending.
" t* " This notation is needed occasionally. It means an instance in time (in an epoch) but not any specific instance. The calculus definition of the derivative of position with respect to time (velocity) is defined "at an instance in time."
" t < 0 " This notation means "all times prior to an event.
" t = 0 " and " t = 0+" These times have a subtle distinction. Each marks the beginning of an event. The time, " t = 0 ", is the instant just before initiation of an event. The notation, " t = 0⁺ ", means at the start time but "started." The superscript, + emphasizes that timing (the clock that measures the duration of the event) has commenced.
" t₁, t₂...and such. " An arbitrary time, " t ", during an event is written as " t ", but when subscripted the meaning is a specific instance of the times of the event (generally greater than "0+" and less than t_fin).
Δt This notation is called "an increment in time." It is an inspecific, finite amount of time. It is sometimes written that is t₁ + Δt = t₂
" t_fin " is use sometimes to denote the termination or ending time of an event.
Initiation of event. Time marks the initiation of an event, that specific, t*, at the start of an event is notated, "t = 0+ " At t* = 0, nothing is happening but just a nano-seconds later, t = 0+, the event is under way.
Increment of Time is a duration or the time between two instances, It is written Δt, meaning the later time minus the initial or t₂ - t₁. Other subscripting used is "t_start, or "t₁" with "t₂" or "t_final."
Differential Time is an idea from calculus. Calculus uses the notation, "dt", to mean a time difference in the limit that it vanishes. "dt" is differential time. The duration of "dt" is zero seconds.

In general, matter exists in space and time. Existence in time means "within some event." Time is an important part, of course. Math, vectors and calculus are the tools of thermodynamic analysis ~ they have their notations. Above are presented "aspects of time" we need. Here (in this writing) even problems with obvious answers, are posed mathematically for analysis. By solving easy problems with precision, one develops a method and sharp analytic tools for the solution of more difficult problems.