Open Physics 2021; 19: 127–133 Research Article Charles C. Hwang* Irreversibility as thermodynamic time https://doi.org/10.1515/phys-2021-0018 Keywords: time, availability, irreversibility, time dilation, received August 30, 2020; accepted February 21, 2021 gravity, entropy Abstract: In Newtonian mechanics, time and space are perceived as absolute entities. In Einstein’s relativity theory, time is frame dependent. Time is also affected by gravitational field and as the field varies in space, 1 Introduction time also varies throughout space. In the present article, the thermodynamic-based time is investigated. In macro- 1.1 Time in classical mechanics scopic view of thermodynamics, energy is conserved in every system or process. On the other hand, exergy fi (availability) is not conserved and can be destroyed, In Newtonian mechanics, the time in the universe is xed [ – ] and “irreversibility” is generated. Since each thermody- regardless of location or epoch 1 4 . This means that all fi namic system may generate different amounts of irrever- events can be regarded as having a distinct and de nite sibility, this quantity is system dependent. The present position in space and occur at a particular moment of article investigates the characteristics of entity irreversi- time. Time as one perceives is absolute and seems to fl bility. (1) It is found that the entity behaves in the similar ow steadily and uniformly regardless of anything external. manner as the clock time in the standard configuration of This moment of time is taken to be the same for observers - inertial frames under Lorentz transformation. (2) It is also everywhere in the universe. Time is an un stretchable found that the entity is affected by gravity fields in the quantity, in terms of which, changes in the whole universe - similar manner as the clock time. We have demonstrated could be uniquely described. The theory constructs a deter that, like clock time, irreversibility is frame dependent, ministic set of mathematical relations that allow prediction and affected by gravity in the similar manner as the clock of the future and past behaviors of moving objects. All that time. For these reasons, we propose to call the irreversi- one needs in order to do this are data in the present bility of the system as the thermodynamic time. The time’s regarding these moving objects. Equations of motion in arrow is automatically satisfied, since irreversibility gene- Newtonian mechanics are invariant under T. ration always proceeds in one direction (toward future). Based on the strength of the findings (1) and (2),apossible application of the irreversibility is an interpretation and management of the aging of biological systems. It is shown 1.2 Time in relativity theory by other authors that entropy generation (equivalent to irreversibility) is a parameter for the human life span. In the special and general theories of relativity, time is ’ Our sensation of time flow may be attributed to the flow stretchable and varied from place to place. Einstein s - of availability and destruction of it through the living mechanics indicates that the time passage for two indi system. viduals moving relative to one another, or experiencing a gravitational field, is different [1,2,5–7]. These theories finally break Newtonian mechanics’ rigid conception, though the flexibility of time passage becomes apparent only at high speeds or in strong gravitational fields. In the following subsections, the rates of clocks differ * Corresponding author: Charles C. Hwang, Department of (1) on moving frames with a constant relative velocity and Mechanical Engineering, University of Pittsburgh, Pittsburgh, ( ) fi ff PA15261, USA, e-mail: [email protected] 2 on uniform gravity elds with di erent strength. In Professor Emeritus; 3005 S. Leisure World Blvd. # 404, Silver later sections, it will be shown that a thermodynamic Spring, MD 20906-8305 quantity irreversibility, I, behaves like time. Open Access. © 2021 Charles C. Hwang, published by DeGruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 128 Charles C. Hwang 1.2.1 Standard configuration [8] their frame. The difference in the rates of two clocks is calculated next. The following frame arrangement is defined for use in ΔΔ1tt′ β22 Δ1 t 1 βt Δ, future discussions. =−=−(−−) Imagine that two rigid reference frames F and F′ are 1 v2 ΔΔtt− ′ =( 1 − 1 − βt2 ) Δ ≃ Δ,t (1.6) in uniform relative motion with velocity v. For both 2 c2 frames, identical units of length and time are used. neglecting magnitude of fourth and higher order [6].If Their time tt, ′ and their Cartesian coordinates x,,y z v =/10 m s , 1/(25.56310vc22 / )= × − 16, showing that the and ′′,,′ form the coordinate systems F :,,,xyzt x yz { } time dilation is very small with low velocity v. and F′ :,,,{xyzt′′′′}. The systems are said to be in stan- dard configuration, if they are arranged in the following - way. The origin of F′ frame moves with velocity v along 1.2.3 Rates of clocks in gravitational field the x-axis of F, the x′-axis coincides with x-axis, while the y- and y′-axes remain parallel, so do the z- and In a uniform gravity field, a clock h sitting on a high shelf z′-axes; and all clocks are set to zero when the two ori- will run faster than a clock ℓ on the floor. If clock h is the gins meet. emitter of light with frequency ωh and clock ℓ is the receiver, Feynman [5]¹ finds the frequency at the receiver as follows. A photon of frequency ωh has energy εωh =ℏ h. 2 1.2.2 Rates of clocks in standard configuration Since emitted energy εh has the gravitational mass εch/ 2 the photon has a mass ℏωch/ and is attracted by the In special relativity, the Lorentz transformation equa- earth. In falling the distance HH=−h Hℓ it gains an addi- 2 tions for the primed and unprimed variables in standard tional energy (ℏ/)ωch gH, so it arrives at the receiver with configuration are as follows: the energy xvt− gH x′ = , (1.1) εωωℓℓ=ℏ =ℏh 1 + . 1 − β2 c2 y′ = yzz,,′ = (1.2) We rewrite the equation as tvxc−/2 ()Rate at the receiver ωℓ t′ = , (1.3) ( ) 1 β2 gH 1.7 − =(Rate of emissionωh ) 1 + . c2 where β =/v c. The inverse of the last equation can be If we write the equation in terms of the time rate written as tvxc′ + ′/ 2 1 1 gH t . ( ) 1 = 1.4 =+2 1 − β2 Δttℓ Δ h c Einstein has calculated the time dilation under the or standard configuration. This proves that time is frame- Δt gH h 1 . ( ) [ ] =+ 2 1.8 dependent 6 . Consider two inertial frames F and in Δtℓ c standard configuration. The frame F′ moves at velocity For H 20 m, gH/= c2152.182 × 10− , that is, for an v relative to the frame F along the x-axis. Consider a = altitude difference of 20 m at the earth’s surface, the clock at rest in F′. Let two events be, 1 and 2, which occur time difference, ΔΔtt− , is only about two parts in at the same point x′ = x′ in F′, indicated by the interval as h ℓ 21 1015. This result proves that time depends on the strength Δttt′ = ′ − ′. Substituting these values in equation (1.4) 21 of a gravity field. Note that the quantity gH/ c2 is non- yields dimensional. ΔΔ1tt′ =− β2 , (1.5) where Δtt=−2 t1. Observers in F observe that the moving clock is running slow. This effect, time dilation, is reci- procal. That is, if a clock is at rest in F, observers in F′ 1 Feynman derived the result with the help of the principle of find that it runs slow as compared with clocks at rest in equivalence. g is assumed constant in this thought experiment. Irreversibility as thermodynamic time 129 2 2 Availability and irreversibility T Δ10 δQ W p Δ, V AI=−∫ −(−)−0 ( ) Tb 2.5 The conservation of energy for a control mass can be 1 expressed as [9,10] heat transfer work interaction irreversibility dEδQδW=−. (2.1) where ΔΔA =+EpVTS00 Δ − Δ. The term irreversibility I(=Tσ) accounts for the destruction of availability due The entropy equation can be written as 0 to irreversible processes within the control mass. δQ Equations for flow availability can be written for an d,S =+δσ (2.2) T open system, including heat transfer and matter flow at [ ] where σ is the entropy production which can be stated as: the boundary surface 9,14 . δσ > 0 internally irreversible process, δσ = 0 internally reversible process, δσ < 0 impossible process. 3 Special features of irreversibility Aquantityavailability (also called exergy, work potential, Arbeitsfähigkeit) has been used by engineers to assess the maximum work that can be obtained for a 3.1 Irreversibility and frame dependence combined system, closed or open, in a given environ- mental condition [9,11,12]. It is known that all macro- We shall demonstrate that the irreversibility I is frame processes are irreversible, and the availability is destroyed. dependent, similar to clock time. Planck² and Einstein³ The destruction of availability is called irreversibility. considered thermodynamic systems which are in the Wall [13] stated that energy is motion or ability to standard configuration [10,15]. First, we note that irrever- produce motion and exergy is work or ability to produce sibility can be expressed as I = T σ [9]. In the standard work. He also stated that time is experienced when 0 configuration of frame F and frame F′, the quantities exergy is destroyed, i.e., an irreversible process, which T and σ are related by the following equations when creates a motion in a specific direction, i.e., the direction 0 ( of time.