Causality is an effect

a r X i v :c o n d -m a t /0011507v 1 [c o n d -m a t .s t a t -m e c h ] 29 N o v 2000For the proceedings of the conference,“Time’s Arrows,Quantum Measurements and Superlumi-nal Behavior,”Naples,Italy,October 2000.To be published by the Italian CNR.Causality is an e?ect L.S.Schulman Physics Department,Clarkson University Potsdam,NY 13699-5820USA email:schulman@https://www.wendangku.net/doc/e64196894.html, ABSTRACT Using symmetric boundary conditions at separated times,I show analyti-cally that both the time ordering of (macroscopic)causality and the direction of entropy increase follow from these boundary conditions.In particular,when the endpoints have low entropy,these arrows of time point away from the ends and toward the middle.Causality in this context means that when perturbations are applied,the e?ect of the perturbation—the macroscopic change in the system’s behavior—is con?ned to one temporal side of the perturbations.These results hold for both mixing and integrable systems,although relaxation for integrable systems is incomplete.Simulations are presented for purposes of illustration.1.Introduction By “causality”I mean that if a system is perturbed the macroscopic e?ect occurs subsequent to the perturbation.There is a lot of baggage in this de?nition.First,I am not talking about the microscopic causality of relativistic quantum ?eld theory,which is a statement about the vanishing of commutators (or anticommu-tators)at spacelike separations.Second,I am trying to avoid the many and subtle de?nitions that have appeared in the philosophical literature,some of which are close to mine,some of which are not.Then there is the word “perturbation,”which suggests a kind of control or free will.Finally,there is the term “macroscopic,”equivalent to a notion of coarse grains,yet another nontrivial concept.De?ning causality in terms of sequential order emphasizes its relation to the thermodynamic arrow of time.Indeed,some consider causality (with similar mean-ing and baggage)to be the primary concept [1,pp.163–164],with other kinds of ordering (in particular,the second law of thermodynamics)consequences of it.

I will take neither of these concepts to be primary,and will instead derive both from a model,or caricature,of the expansion of the universe.This follows the ideas of Gold [2]and my own elaboration of them [3,4],in particular emphasizing the notion of two-time boundary conditions.It is clear that it would be pointless

to study causality as de?ned above using initial values for macroscopic problems, since such a formulation forces the e?ect of a perturbation to be subsequent.So in studying causality,as in studying the arrow of time,one should formulate the problem time-symmetrically if one’s conclusions are to be noncircular.

I will?nd that both macroscopic causality and the second law,meaning entropy increase,can be derived in the appropriate two-time boundary condition context. For su?ciently chaotic dynamical systems both features?ow naturally from the formalism.For integrable systems,relaxation can be imposed by averaging over frequencies.But with future conditioning additional time scales enter,and while one can still get relaxation and causality,there is not the same simplicity as for chaotic systems.

In Sec.2I introduce the general context for this discussion as well as notation. In the following section there is an analytic derivation of symmetric entropy increase for systems having appropriate two-time boundary conditions.Causality,treated in Sec.4,is established using the same methods.In the last section numerical work is shown to illustrate the results of the previous sections.There are two appendices. In the?rst I give a general derivation of entropy increase when coarse graining is implemented at each time step.This is a master equation approach and is mainly pedagogical.In the second appendix I indicate how the notion of“perturbation”need not depend on philosophical questions concerning free will.

2.Framework and notation

As in previous publications[3–6],my context is a two time boundary value problem in which macroscopic data are speci?ed at an early time,“0,”and a late time,“T.”At both boundary times the system is in a restricted state(i.e.,low entropy).For the systems previously studied the entropy increases,with varying degrees of monotonicity,away from both boundary times.Moreover,for chaotic systems,if the interval between the boundary times exceeds twice the system’s relaxation time,the initial relaxation is macroscopically indistinguishable from un conditioned time evolution.Furthermore,the evolution away from the?nal point (i.e.,from T to smaller values of the parameter t)is the symmetric image of the initial relaxation—this assertion is true even with conditions on the time evolution that are weaker than time reversal invariance.All these features have been used to argue for Gold’s thesis.In some of the references above I have elaborated on my rationale for taking this approach,and will not repeat the argument here.Most of my previous demonstrations have used the cat map[7]as the dynamical system, and computer simulations to provide the evidence.

In this article I will argue more generally,extending both the systems studied and the method of justi?cation.In e?ect this explains why the simulations work, although a discussion without explicit equations occurs in[4]and embodies the essential ideas to be presented below.

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Consider classical mechanics on a(phase)space?.Letμbe the measure on ?andμ(?)=1.Let the dynamics be given by a measure-preserving mapφ(t)on ?,withφ(t)(ω)the time-t image of an initial pointω∈?.The time parameter,t, may be either continuous or discrete.

The notion of“macroscopic”is provided by a coarse graining on?.This is a ?nite set of sets of strictly positive measure that cover?:{?α},α=1,...,G,with ∪α?α=?,?α∩?β=?forα=β.Letχαbe the characteristic function of?αand let vα=μ(?α).If f is a function on?,its coarse graining is de?ned to be f(ω)≡ αχα(ω)vα.

(1) Thus f αis the average of f on?αand ?f= ? f.

Let the system’s distribution in?be described by a density functionρ(ω).One can think of this distribution in more than one way.In terms of the ideal gas of cat map atoms that I have used before,ρcan be thought of as the density of atoms on the phase space,I2,on which a single cat map lives.(In this caseρis a sum ofδ-functions.)More generally,one can think of?as the6N-dimensional phase space of N particles in three space dimensions.In this way there is no restriction in allowing interactions among the particles.

If one takes a primitive notion of entropy as

S prim=? ?ρ(ω)log(ρ(ω))dμ,

then S prim is constant in time,trivially by virtue of the measure preserving property ofφ(t)(and its invertibility).The entropy that I will use for studying irreversibility involves coarse graining and is de?ned as

S(ρ)=S prim( ρ)=? ? ρlog ρdμ.(2)

It is easy to show that

S(ρ)=S(ρα|vα),

where,as in Eq.(1),ρα= ?αρdμ,and the function S(p|q)is the relative entropy de?ned by

S(p|q)≡? x p(x)log p(x)

3.Time-dependence of the entropy,with and without future conditioning

The system is required to start(t=0)in a subset?0??and end(t=T)in a subset?T??.The points of?satisfying this two-time boundary condition are

?=?0∩φ(?T)(?T).(3) The set?can be empty.I have argued though[9,4]that for chaotic dynamics and for su?ciently long times T there exist solutions,i.e.,?=?.Moreover,for such times

μ(?)～μ(?0)μ(?T).(4) To see how this comes about,consider mixing dynamics.The mapφ(t)is mixing if

lim

t→∞

μ A∩φ(t)(B) =μ(A)μ(B)(5)

for measurable subsets A and B of?.For such systems Eq.(4)will be satis?ed in the t→∞limit.This limit says nothing about rates of convergence,but I will assume that there is some timeτsuch that the decorrelation condition(Eq.(5)) holds to good accuracy for t≥τ[10].The set?will therefore be nonempty for t≥τ.Underφ(t),?becomes

?(t)=φ(t)(?0)∩φ(t?T)(?T).

To calculate the entropy,the density,which wasρ(0)=χ?/μ(?)at time-0,must be coarse grained.The important quantity for the entropy calculation is

ρα(t)=μ(?α∩?(t))

μ(?)

.

If T?t>τthen the following will hold

μ ?α∩φ(t)(?0)∩φ(t?T)(?T) =μ ?α∩φ(t)(?0) μ φ(t?T)(?T) ,

μ(?)=μ(?0)μ φ(?T)(?T) .

Using the measure-preserving property ofφ(t),the factorsμ(?T)in both numerator and denominator ofραcancel,leading to

ρα=μ ?α∩φ(t)(?0) μ(?0).

This is precisely what one gets without future conditioning,so that all macroscopic quantities,and in particular the entropy,are indistinguishable from their uncondi-tioned values.

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Working backward from time-T one obtains an analogous result.De?ne a variable s≡T?t and set??(s)≡?(T?s).Then

??(s)=φ(T?s)(?0)∩φ(?s)(?T).

If s satis?es T?s>τ,then when the density associated with??(s)is calculated,its dependence on?0will drop out.It follows that

ρα(s)=μ φ(?s)(?T) μ(?T).

For a time-reversal invariant dynamics this will give the entropy the same time de-pendence coming back from T as going forward from0.It is interesting that the cat map is not strictly time-reversal invariant(by de?nitions of the form given in [11])but,as I have shown repeatedly,its entropy as a function of time is symmetric. The reason is that the Lyapunov exponent is the same for the map and its inverse. For the cat map,there isn’t much choice:the2×2matrix has only two eigenvalues and their product is unity.But I expect the similarity of macroscopic dynamics in both directions to obtain even for richer systems.Thus,comparing true phys-ical dynamics with its time-reversed counterpart,ordinary macroscopic relaxation should be the same,yielding symmetric entropy dependence.I justify this expecta-tion by the absence(so far)of any time-reversal or CP violating observations at the atomic level,as well as the assumption that ordinary physical relaxation processes, accounting for the thermodynamic arrow of our experience,occur at grosser levels than those at which CP violation has been detected.

It is worth putting into words the essence of the mathematical argument just given.The set?is a subset of?0;which points of?0are also in?is determined by the choppy characteristic function of the setφ(?T)(?T).For long enough times,T,the good points of?are Poisson distributed within?0[4].Thus following?forward in time(withφ)is like following a random subset of?0.But such time evolution is one way of studying?0itself.If you wanted to do a Monte Carlo study for the evolution of?0,your technique would be to follow the time dependence of a random subset. The pseudo-randomness imposed by the characteristic function ofφ(?T)(?T)is not worse than other kinds of pseudo-randomness.

The same pseudo-randomness holds for?(t)(t>0),provided the time to the ?nal point,T?t,is greater thanτ.I have used the mixing property to argue for randomness,but I expect weaker conditions of ergodicity to be su?cient in physically relevant situations.

Integrable systems(relaxation)

Without mixing or some kind of ergodicity the foregoing arguments fail.How-ever,harmonic oscillators can be quite useful in studies of relaxation[12],although in previous two-time boundary value studies[3]de?ciencies were noted.The gen-eral idea is that although an individual oscillator does not spread in phase space,if enough di?erent frequencies are taken there is relaxation.

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Rather than work with sets,as above,I consider an“ideal gas”of N oscillators, with oscillator#k having position x(k)and frequencyν(k).(For convenience I take the period of these oscillators to be1(rather than2π)and use frequency rather than angular frequency.)Time evolution is given by x(k)(t)=x(k)0+ν(k)t(mod1). The boundary conditions are

0≤x(k)0≤δx&0≤x(k)(T)≤δx,with x(k)(T)=x(k)0+ν(k)T(mod1),

ν0≤ν(k)≤ν0+δν(νdoes not change in time).

(6)

Both x(k)andν(k)can be randomly selected consistent with these conditions. From the?nal-time condition on x it follows that for su?ciently large T there is a nonempty?nite set of integers{n?}so that

?x(k)0

T ≤

δx?x(k)0

x(k)(T/2)=x(k)0+n/2+β/2.For even n this means that many of the points are back in the original interval,or close to it.Thus the entropy will drop.The same happens,but less dramatically,for other divisors.Finally,there is an inherent weakness in any oscillator equilibrium,in that only half the dynamical variables relax at all—the frequencies(ν)do not change.

In terms of the big bang-big crunch cosmological model considered in[4–6] these defects are probably irrelevant.It appears that the“oscillators”in our cos-mos are mostly the degrees of freedom of the electromagnetic?eld.These reach equilibrium through being coupled to massive matter,which presumably does re-lax appropriately.If they do satisfy a two-time boundary condition with,say,the boundary times at the decoupling epoch and its pre-big crunch partner,then I would not expect the timing to be so precise and coincident that one would get photon entropy-lowering at the cosmological midpoint(as in our“even n”condition above). Moreover,photons do not equilibrate very well:witness the preservation of indi-cations of spatial structure as deduced from cosmic background radiation.On the other hand,the spectrum of this radiation corresponds very well to equilibrium,the reason being interaction with matter prior to decoupling.

4.Causality and peturbations

The notion of macroscopic causality used here involves a perturbation.One imposes two-time boundary conditions and considers dynamical evolution with both unperturbed and perturbed dynamics.When solving the same boundary value problem,these rules will select di?erent microscopic solutions.Although I will consider perturbations occurring only at a single moment in time,the microscopic solutions will(in general)di?er everywhere.But it is the macroscopic solutions that allow a notion of causality.In principle macroscopic behavior could also di?er at all times(except for the boundaries),but in a system with causality they will di?er on only one side of the perturbation.For the usual causality,they will di?er only after the perturbation.But we will also?nd that they can di?er only before, where in this sentence and the last the words“before”and“after”are de?ned with respect to a microscopic time parameter,that,as will be seen,may di?er from the natural thermodynamic time.

There is a delicate point here that is discussed in Appendix B.The term “perturbation”suggests free will,while two-time boundary conditions sound like the opposite.Resolving issues of free will is not my objective,and the appendix is devoted to formulating the concept of perturbation in a purely physical context.

Although I will later give examples(?gures)in terms of discrete time,for formal purposes it is easiest to work in continuous time and to imagine that the perturbation is instantaneous.The time interval for the boundary value problem is[0,T].Call the unperturbed system A;its history,time evolution,dynamics and boundary conditions are exactly as described in the previous section.That is,it

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evolves underφ(t),its boundary conditions are?0and?T,and its microstates are in the set

?A=?0∩φ(?T)(?T)(8) (formerly called?).System B,the perturbed case,has an additional transformation act on it at time-t0.Call this transformationψ.It should not be dissipative—I do not want the arrow to arise from such an asymmetry alone[13].ψis thus invertible and measure preserving.Successful solutions must go from?0to?T under the transformationφ(T?t0)ψφ(t0).The microstates for system B are therefore in

?B=?0∩φ(?t0)ψ?1φ(?T+t0)(?T)(9) Clearly,?A and?B are di?erent.But as I shall now show,for mixing dynamics and for su?ciently large T,the following hold:1)for t0close to0,the only di?er-ences in macroscopic behavior between A and B are for t>t0;2)for t0close to T,the only di?erences in macroscopic behavior between A and B are for t

The proof is nearly the same as that of the previous section.Again we use the timeτsuch that the mixing decorrelation holds for time intervals longer thanτ. First consider t0close to0.The observable macroscopic quantities are the densities in grain-?α,which are,for t

ρAα(t)=μ ?α∩φ(t)(?0)∩φ(t?T)(?T) μ(?A),

ρBα(t)=μ ?α∩φ(t)(?0)∩ φ(t?t0)ψ?1φ(t0?T) (?T) μ(?B).

As before,the mixing property,for T?t>τ,yieldsρAα(t)=μ ?α∩φ(t)(?0) /μ(?0), which is the initial-value-only macroscopic time evolution.ForρBα,the only di?er-ence is to add a step,ψ?1.Unlessψ?1is diabolically contrived to undoφ(?u)for large u,this will not a?ect the argument that showed that the dependence on?T disappears.Thus A and B have the same macrostates before t0.

For t>t0,ρAα(t)continues its behavior as before.ForρBα(t)things are di?erent:ρBα(t)=μ ?α∩ φ(t?t0)ψφ(t0) (?0)∩φ(t?T)(?T) μ(?B)(t>t0). Now I require T?t>τ.If this is satis?ed the?T dependence drops out and

ρBα(t)=μ ?α∩ φ(t?t0)ψφ(t0) (?0) μ(?0).

The shows that the e?ect ofψis the usual initial-conditions-only phenomenon.

If we repeat these arguments for t such that T?t is small,then just as we showed in Sec.3,the e?ect ofψwill only be at times t less than t0.

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This manifestation of causality has a clear intuitive origin.As the perturbation time,t0,choose a value small enough that the system has not equilibrated[14].All points,a∈?A and b∈?B,start in?0and end in?T.Working backward from t0, what can b do?It must get to?0.Since t0is less than the relaxation time,the places it can be are essentially the same places that a can be.However,after the perturbation the need to arrive in?T places no macroscopic restriction on b,because from any coarse grain in?you can?nd your way into?T.This is precisely because working backward from T,the set?T spreads throughout?in time T?t0(and in particularφ(t0?T)?T enters the coarse grain into whichψwould send b if there were no future conditioning).Thus,satisfying the changed boundary conditions is accomplished by keeping a and b close to one another before t0,and allowing the perturbation a free hand in moving b away from a,after t0.

Integrable systems(causality)

As before,without mixing or some kind of ergodicity our arguments fail.Nev-ertheless,just as frequency smearing gave relaxation,however imperfect,it can give causality.Again an extended time scale is needed,but the intuitive reasoning just given continues to hold in the integrable case as well.

Consider a particular example,an oscillator of the sort discussed in Sec.3.Take δx so small that the condition in Eq.(6)forces all the points to have essentially the time dependence,x=νt,withνT=n.The angular frequencyνtherefore satis?esν=n/T,with n selected so thatν0≤ν≤ν0+δν;for large T,this allows an extensive range of n values.Now consider the following perturbation:at the moment t0,x is displaced by a macroscopic angleγ,i.e.,γ>1/G.Solving the same boundary value problem gives x=νt before t0,and x=νt+γafter t0.With the perturbation,νmust satisfyν=n/T?γ/T,again yielding an extensive range of n values for large T.The di?erence between the two ranges of n values isγ/T, which for large enough T will be a small fraction of all n values that are common to the perturbed and unperturbed motion.Such n are henceforth dropped from consideration.

For n values that are common to the two solution sets,the di?erence between solutions with the same n arises from theγ-dependent di?erence inν:

,(10) E?ect n=x unperturbed?x perturbed= γt/T t

?(1?t/T)γt>t0

which is independent of n.It follows that there is a di?erence between perturbed and unperturbed motion that is of orderγthrough most of the time period[0,T]. The e?ect of the perturbation is felt both before and after.It thus appears that there is no causality,but closer consideration shows this conclusion to be wrong.

Recall that it is only meaningful to consider perturbations that take place before the system has relaxed(or close enough to T that the reverse process has commenced).Thus the perturbation should occur for t0<τosc=1/δν.On the other

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conditioning.For the left?gure(2a)there is no perturbation.In the middle(2b) there is a perturbation at time3.On the right(2c)the perturbation is nominally at time14,although because of the way entropy is calculated(after a time step,in terms of the nonthermodynamic parameter t)it is e?ectively at time131

hand,for full relaxation the value of T should be greater than G/δν,as discussed in Sec.3.From Eq.(10)the maximum value of the precursor—the noncausal term—is t0/T,just before the perturbation.These considerations are combined to yield

1

T <

τosc

G

.

But the size of a coarse grain is1/G,so that this precursor is in fact microscopic.

Double arrow systems

In[5]I showed that causality obtains in opposite directions in systems con-taining opposite arrows.The general principle is the same as that presented here although a detailed presentation would be more complicated by virtue of the si-multaneous presence of two directions for causality.I will not provide an analytic demonstration and only mention this matter here for completeness.

5.Numerical illustrations

Although the purpose of the present article is to go beyond the numerical simulations of previous publications,I will illustrate the phenomena studied here.

In Fig.1I show the e?ect of using two-time boundary values on the dynamics of the cat map,φC.(This is a map of the unit square into itself with the rule: x′≡x+y,y′≡x+2y,mod1.It is a mixing transformation,intensively exploited in ergodic theory[7]and I have used it as an example for two-time boundary value problems in many places,[4],etc.)

On the left(1a)there is no perturbation.The boundary conditions are that the system must be in a particular coarse grain(of size0.1×0.1)at times0and16.

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ing.The left?gure(2a)shows an entire run of200time steps.Both perturbed and unperturbed motion appear.They di?er in many places.Note also the half-time depression in entropy,as well as other,smaller reductions.In the middle(2b)is shown only the?rst few time steps.The perturbation is at time-4.Causality is evident.On the right(2c)only50time steps are used.Although from the previous ?gures it is clear that the entropy can reach its maximum values within about10 time steps,when the conditioning time is50(as in2c)the system cannot get near the equilibrium value.(All?gures show the same numerical range of entropy.)

2.The deviation between

the perturbed and unperturbed entropy is for times3and4(by time-5both systems are in equilibrium).Because the perturbed system received a bigger kick at time-3 its entropy increases more rapidly.

The point of this?gure is that the di?erence between the curves is con?ned to times later than the perturbation.The system shows causality.

The right hand?gure(1c)shows a system that is perturbed at time-14.As before,the entropy-calculating convention makes this e?ectively a perturbation at time131

Finally I show what happens for harmonic oscillators.The perturbation is slightly di?erent from that studied analytically above.Rather than a displacement, the system advances by3νinstead ofν.The results are essentially the same and by this small change one also can see a level of robustness of the phenomenon.

For Fig.2there are25coarse grains along the“x”direction and the frequency interval is of width1/10.Thus unconditioned relaxation should take place in about 10time steps,but full equilibration should take about250.For Fig.2a and2b (which are from the same run)both aspects are evident.With200time steps the system does approach S=0and the relaxation time is about10(as is seen more easily in Fig.2b).On the other hand,in Fig.2c,with conditioning for50time steps, S is far from0,so that the potential for10-time-step relaxation is thwarted by the future condition.In all cases there is a perturbation at time-4.Fig.2b clearly shows that there is causality in this case.On the other hand,for the third?gure, the system’s relaxation is so compromised that the action of the perturbation takes place when the system has reached its maximum,although reduced,entropy level. Acknowledgements

I am grateful to the Istituto Italiano per gli Studi Filoso?ci,Naples,for hosting the conference where this material was presented.My research is supported in part by the United States National Science Foundation grant PHY9721459. Appendix A.Entropy increase,stochastic dynamics and coarse graining The formalism developed above is useful for a general derivation of entropy nondecrease.The derivation also holds for quantum mechanics.

Proposition:Coarse graining a distribution function,evolving it forward,and then again coarse graining,either increases the entropy or leaves it unchanged.

Let the distribution function for a classical system at time-0beρ.It is coarse grained to yield ρ,which is taken asρ(0).Thus

ρ(0)= χα

ρα

vα

withχ?αthe characteristic function of?α≡φ(t)(?α).Now coarse grain again.This is the step where entropy nondecrease is forced,and I discuss its physical signi?cance

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Table1.Classical-quantum correspondence for the entropy increase proposition.

?H(Hilbert space)ρρ(density matrix)

?αHα(subspace)μTrace

χαPα(projector)vαdimension of Hα

φ(t)U t

μ ?β∩φ(t)(?α) = χβ

vαvβ

ρα,withρα=Tr Pαρand vα=Tr Pα.

vα

Entropy is again S(ρα|vα).(The v s no longer sum to unity,but this makes no essential di?erence.)Time evolution is given by a unitary operator,U t,acting in the usual way:ρ(t)=U tρ(0)U?t.Carrying through the same steps as for the

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classical case,coarse graining,evolving in time and coarse graining again,leads to the same equations,but with the matrix“R”now given by

R(β,α)=Tr PβU t PαU?t vα.

Stochasiticity of R is readily established and entropy nondecrease follows as above.

Appendix B.Perturbation in a deterministic system

A perturbation is often thought of as an act of control.In contrast,it would seem that imposing future conditions denies the possibility of modi?ed evolution. Put di?erently,perturbing is an act of free will;future conditions—along with the deterministic context for their imposition—?y in the face of that concept.

This is not the place for a discussion of free will,except to mention that contrary to the impression of many physicists,some philosophers?nd justi?cation for free will,not from the supposed indeterminism of quantum mechanics,but from chaos in deterministic dynamical systems[17,p.152].

But one need not imagine an independent actor to obtain the“perturbation”of Sec.4.Consider the following situation,within the context of the cosmological scenario described in[4]or[6].Two systems,A and B,are small parts of a big universe,but they are isolated,or nearly so,between the times to be used for the boundary value problem.The actual macroscopic boundary values for the two of them are the same.Now imagine that one of them,say B,is not perfectly isolated, but at some intermediate time,t0,in its history,is struck by something coming in from the outside.This“outside”is simply another part of the universe,not A and not B.Its main properties are its lack of correlation with what is otherwise happening to A and B,and its ability to pack a macroscopic wallop in B.Despite the outside force,I still require the same boundary values for A and B.

Now compare the macroscopic motions of A and of B.Were it not for the outside force,they should be the same.With the force,having changes occur only on one(temporal)side of the perturbation is what I call macroscopic causality.

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[8]This de?nition di?ers slightly from that used in[4],etc.The di?erence is ? vαlog vα.Thus the maximum(old de?nition)entropy for G equal-volume coarse grains is log G.With the de?nition here the maximum is zero.

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[10]I will not try to look for minimal values ofτ,since keeping track of this would

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equilibrium statistical mechanics,J.Math.Phys.37,3897(1996).

[17]D.C.Dennett,Elbow Room:The Varieties of Free Will Worth Wanting(MIT

Press,Cambridge,Mass.,1984).

15

全国翻译价格

全国翻译价格 关于全国各地区翻译价格我们根据客户的不同需求和具体情况，提供多种等级和特色的翻译服务，供客户选择：（注：以下报价均为参考价格，精确报价将根据稿件内容的难度、技术处理的复杂程度和时限要求的缓急而定。

品质控制 坚持高端定位是外语通翻译的核心要素，追求高品质翻译需要译员具备深厚的语言功底和专业背景知 识，更需要严格的质量控制体系来管理这一过程： 外语通六阶梯质量控制体系 第一阶梯：译文评估承接 分析稿件性质、用途要求、商务背景、专业术语、数量和交稿时间等，确定是否有100%的把握承接， 否则坚决放弃，以免因质量或交稿时间耽误客户和影响品牌形象。 第二阶梯：专业译员翻译 专业背景的译员只专注于一个行业领域的精准翻译，项目经理根据译文评估，从外语通全球译员库中 分析挑选多名此行业的专业译员成立项目组，统一专业术语和标准，协同翻译。 第三阶梯：翻译质量监控 项目经理监控翻译进展，每日集中疑难词汇，请签约专家释疑。每日抽查译文质量，及时解决译文质 量问题。 第四阶梯：译文校对排版 汇总所有译文，查错补漏，进一步统一术语，按原文进行排版，形成完整初稿。 第五阶梯：专家译审修改 专家译审对翻译初稿进行翻译准确性审核，确保译稿忠于原文，专业词汇纯正地道。 六阶梯：外籍母语润色第 在华外籍翻译（外译中稿件由中文功底深厚的编辑）对译稿的语法、词汇进行修正和润色，确保译稿 纯正、地道，达到母语品质。 外语通翻译严格执行《ISO译文质量体系》，《翻译质量国家标准GB/T 19682-2005》： 译文质量标准Ⅲ类通用笔译Ⅱ类专业笔译Ⅰ类高级笔译译文用途内容概要、参考资料一般文件和材料正式文件、法律文书、出版物错漏译率小于5‰小于2‰0‰ 译员经验3年以上5年以上8年以上 译员学历硕士以上硕士以上硕士以上 行业背景常识业内资深 海外背景无/短期中期长期 译文校对有有有 专家译审无有有 母语润色无无有 译文排版简单排版详细排版出版级别

翻译公司收费标准

翻译公司收费标准 1.客户需要翻译的目标语言的普遍性和稀缺性可能导致非常 不同的费用。英语比较普遍，需求大，市场专业的英语翻译人 才也很多，翻译公司无论是从降价到抢占市场，还是成本核算 来考虑，英语收费都比较合理和透明。 其他诸如法语、德语、日语、俄语排在第二梯队，翻译公司收 费标准一般都是200-280元，视稿件专业度和数量略有调整； 意大利，西班牙，越南，泰文等东南亚语种已经接近稀有语 种了，翻译报价至少300元千字起。 2.根据翻译项目类型 常见的翻译方法主要包括翻译翻译、同声传译、本地翻译、口译翻译等，翻译项目自然是不同的收费。 3.根据翻译项目时长 这一时期的持续时间主要是指项目长度：同声传译、会议翻译、商务洽谈、双语主持人、口译、护送翻译、展览翻译，当然，视频翻译、音频翻译按时间计算的时间和会议类型是一个重要因素，是翻译时间决定翻译价格的一个重要因素。 4.根据翻译项目字数

翻译项目的字数是影响收费的重要因素之一，翻译字数主要对于笔译而言，例如：文件翻译、图书翻译、资料翻译、画册翻译等等，这些文件资料的字数决定了项目的翻译价格和翻译收费标准。 5.根据翻译项目语种 主流语种：英语、日语、韩语等和小语种：阿拉伯语、希腊语、印尼语等的翻译收费标准区别。我们知道：“物以稀为贵，”所以小语种的翻译报价会比主流语种收费要高的。 6.根据翻译项目难易程度 对于翻译公司来说，翻译费在很大程度上取决于翻译的难度程度，不同的行业术语不同，难度不同; 专业翻译公司将根据翻译人员的翻译水平、专业知识、翻译经验等方式来评价自己的翻译团队，高层次的翻译人员当然都是高收费; 如通用翻译、精细翻译、出版层次等不同类型的翻译报价不同，稿件的行业领域、材料难度、选择翻译类型等都是决定翻译公司收费标准的因素。

英文合同翻译价格 英文合同翻译需要多少钱

英文合同翻译价格英文合同翻译需要多少钱 在企业的经营过程中，有时候可能会涉及到翻译这个问题，但是一般的小企业并没有专门的人去做这件事情，大部分都是外包。那么对于企业来讲，翻译一份英文合同需要多少钱呢？作为浙江省最大的翻译公司，以琳翻译就在这里为大家解读一下。 一般来讲，翻译这项服务都是以字数来计价的，市场上的一般的价格是50-80元/千字，这是一个基本的价格。但是不同的公司的专业性质不一样的话，所给出的价格也是不一样的。对于公司的衡量标准来讲，影响价格的因素主要有：公司的资历、翻译人员的专业性、翻译文件的种类、难度等。所以，如果你需要去找翻译公司去服务，那么就需要考虑这些方面的东西。而对于合同这种文件，对于公司来讲是十分重要的，所以也需要去找专业的公司去进行翻译，如果是找一个资质不够的公司或者团队，那么就可能产生一些意想不到的问题，从而影响到公司的最终利益。 下面，我们来看看以琳翻译给出的翻译的价格。 从上面的价格可以看出，以琳翻译给出的价格是高于一般市场上的价格的，最低级别的翻译是160元/千字，然后分为A、B、C三级。C级译稿为普通中籍译员+中籍译员审核，满足客户对译文的普通要求。这是对于一般的合同而言的，但是如果是部分专业性质较强或者要求比较高的译文的话，那么可以选择更高级别的翻译，当然价格还是相对比较高的。 那么以琳翻译的资质是怎么样呢？我们再来看一下。 杭州以琳翻译有限公司是浙江省最大的实体翻译公司、中国翻译协会单位会员、美国翻译协会会员、全国翻译专业硕士研究生教育实习基地、西博会指定合作伙伴、以琳杭州翻译公司翻译团队成员均具有五年以上专业翻译、项目管理经验，绝大部分成员具有十年以上行业翻译经验。翻译服务涵盖英语、法语、韩语、日语、德语、俄语、西班牙语、葡萄牙语、

专业英文翻译中文收费标准

精诚英语翻译报价50-80元千字（市场价格100左右 精诚英语翻译工作室是由众多英语方面精英组成的翻译团队,一直致力于为广大中小企业和个人提供专业低价中英文翻译服务。价格是我们永远的优势！！！！最低价格支付宝担保交易，让你省钱又放心接受试译！！自信源于专业可以百度搜索精诚英语翻译找到我们 选择我们的理由：可以百度搜索精诚英语翻译找到我们 1.保证价格最低，团队网络化运作，无需经营成本，可以通过低价让利于客户。（有些客户看到这么低的价格还不敢相信，但是对于我们来说是完全可以接受的。） 2.保证准时、保密、准确 3.接受淘宝交易，让您没有任何担忧。 4.长期翻译经验，保证质量让您满意。 龚如心遗产案虽然告一段落，「遗产」二字仍然成为近日香港的焦点。新春期间，民政事务局局长曾德成表示，政府将展开全港非物质文化遗产首期普查，希望市民为遗产清单提出建议。 「遗产」是「资产」？ 近五、六年间，香港对保护本地小区和文化传统的意识高涨，现在政府带头要列一个「非物质文化遗产」清单，理应是很受欢迎之举。不过普查尚未展开，就引来学者争议，其中单是「非物质文化遗产」这个译名，就引起不少误会。 「非物质文化遗产」的原文是intangible cultural heritage（英文）或patrimoine culturel immateriel （法文），是联合国在1997年以尊重多元文化为大原则而提出的概念，并由联合国教科文组织制定「保护非物质文化遗产公约」，2006年生效。 「非物质文化遗产」是中国大陆的翻译，香港有学者不约而同就「非物质」和「遗产」二字提出质疑。香港城市大学中国文化中心主任郑培凯早在2005年就大声疾呼译名不妥。他认为原文heritage/patrimoine的意义是「传承」而非资产，不容易引发出财产的概念。而现在约定俗成译作「遗产」，容易令人觉得祖宗留下的东西，是可以变卖和投资的生财工具，与联合国提出的文化传承精神背道而驰。郑教授认识，正确的译名是「非物质文化承继」或「非实物文化传承」。另一位民俗学研究者陈云进一步指出，intangible「乃触摸不到的事，无形无相之事」，应用「精神价值」代之，「非物质」有消灭了精神之嫌，所以中国人应堂堂正正将之翻译为「无形文化传承」。 姗姗来迟的「遗产」 不论是「非物质」还是「无形」，「遗产」还是「承传」，即使公约成员国中国曲译甚至错译，香港特区政府还是只能照单全收。而且，随之而来的不止是字面的斟酌，而是「遗产」的搜寻和管理问题。 中国自2005年起，就开始非物质文化遗产（由于这个名称已约定俗成，故下文仍沿用之，并简称为「非遗」）普查，并陆续列出清单。香港也在翌年提出编制非遗清单，但却延至去年才聘专家普查，估计最快要2012年才完成。 非遗普查尚未展开，在国家文化部的再三邀请（或是说催促？）下，去年九月，香港终于申请将长洲太平清醮、大澳端午游涌、大坑舞火龙和香港潮人盂兰胜会列为第三批国家级非遗，预计今年六月有结果。 其实香港已错过了2006和2008年首批和第二批的申报机会，所以，至目前为止，在中国的文化版图上，香港是唯一没有任何有形和无形「遗产」的主要城市／特区，就连比邻的澳门也凭神像雕刻工艺获得2008年国家级非遗之「奖项」。 有人说非遗不过是人有我有，纯粹锦上添花；也有人说，中国在维护主权和领土完整的概念下，又怎能在文化层面少了香港一席？香港能够「出产」一个非遗，中国在全球的文化图谱中就多一个筹码。 姑勿论背后原因为何，由于「保护非物质文化遗产公约」也适用于香港，香港特区政府就有责任找出和保护濒危失传、与社会关系密切及具香港独特性的文化传统。现在起步虽迟，但为时未晚。 「遗产」的管理问题 不过，既然政府要展开普查，另一个问题来了。民间传统应该是属于民间的，并由民间自行发展，还是属于官方，由政府承担保护与管理？ 据政府委聘负责首期普查的香港科技大学华南研究中心主任廖迪生表示，政府至今仍未有任何政策配合或承诺给予全面的保护，所以，即使清单出炉，有些遗产仍有可能难逃「破产」的命运。他强调制作非遗清单只是第一步，更重要的是如何保护这些项目。 再问民政事务局，曾德成局长除了曾向立法会议员表示，制定清单是向国家文化部申请列为国家级非遗的第一步，进而再向联合国教科文组织提出申报为世界非物质文化遗产，他所提出的，就是以遗产作招徕吸引外地游客，「以提升香港作为旅游目的地的吸引力」。 这才是令人担心的地方。「非遗」这个金漆招牌在中国许多地方都有点石成金之效。戴上这个冠冕，民俗文化很容易沦为生财工具、游客的消费品，连婚嫁仪式也可用来表演，完全违背了保护非遗的原意。曾德成之言，是否意味着香港也要跟着祖国一起走上同一条路？

英文翻译价格

英文翻译价格 根据以英文作为母语的人数计算，英文是最多国家使用的官方语言，英语也是世界上最广泛的第二语言，也是欧盟，最多国际组织和英联邦国家的官方语言之一。但仅拥有世界第二位的母语使用者，少于标准汉语。上两个世纪英国和美国在文化、经济、军事、政治和科学上的领先地位使得英语成为一种国际语言。如今，许多国际场合都使用英语做为沟通媒介。英语也是与电脑联系最密切的语言，大多数编程语言都与英语有联系，而且随着网络的使用，使英文的使用更普及。英语是联合国的工作语言之一。 为了方便大家了解英文翻译价格，小编在目前汇集最多翻译团队的高校译云上面获得了不同翻译精英团队所展示的价格。 暨南大学翻译中心：中英---普稿---150---千字英中---普稿---250---千字 武汉理工大学-外国语学院MTI翻译中心 ：中英互译中英130-150 英中100-130 华中科技大学-翻译研究中心 ：中英互译中英120-150 英中100-120 湖南科技大学MTI中心：中英---普稿---150---千字 上海师大外国语学院翻译中心： 中英---普稿---200元---千字英语普通文本译成汉语---120元---千字西南大学翻译中心：中英---普稿----300---千字英中---普稿---200---千字 上海理工大学MTI翻译中心：中英---普稿---100---千字 南京财经大学外国语学院翻译研究中心：中英---普稿---100---千字 一般英文翻译价格是是在100—300元每千字，根据译员质量、翻译内容、需要的时间等都会有一定的波动，所以以上价格供大家参考，具体的可以准备好稿件了去问，这样会更加准确一些。

翻译服务收费标准

翻译服务收费标准 一、笔译人民币元/千字中文( 加急加收30% —70% ，专业加收50% ) 语种中译外外译中外译外 英语170 140 面议 日语170 140 韩语190 160 德语220 180 俄语220 180 法语220 180 意大利语280 250 西班牙语280 250 葡萄牙语290 260 阿拉伯语350 320 越南语430 400 荷兰语510 460 波兰语380-480 360-40 塞尔维亚语370-470 420-530 泰国语260-380 280-520 老挝语320-420 370-480 印度语320-420 370-480 希腊语370-470 420-530 哈萨克语280-380 300-410 瑞典语300-400 340-450 丹麦语320-420 370-470 印度尼西亚语330-450 350-460 蒙古语300-400 350-460 1、字数计算：以中文版稿件在Windows word文档显示的字符数（不计空格）为基准。也即包含了标点符号，因其为理解语义的必需。 2、图表计算：图表按每个A4页面，按页酌情计收排版费用。 3、外文互译：按照中文换算，即每个拉丁单词乘以二等于相应的中文字数。 4、日翻译量：正常翻译量3000-5000字/日/人，超过正常翻译量按专业难易受20%加急费． 5、付款方式：按预算总价的20%收取定金，按译后准确字数计总价并交稿付款。 6、注意事项：出差在原价格上增加20%，客户负责翻译的交通、食宿和安全费用。 二、口译价格： (1) 交传报价（元/人/天，加小时按100-150元/小时加收费用）类型英语德、日、法、俄、韩小语种 一般活动700 800 1500 商务活动500-1200 500-1500 800-3000 中小型会议1200-3000 1500-3000 2500-3000 大型会议1200-4000 2500-6000 4000-9000 (2) 同传报价（元/人/天） 类别中-英互译日、韩、德、俄、法、韩-中互译小语种-中互译 商务会议5000-8000 6000-10000 8000-10000 中小型会议5500-8000 7000-12000 8000-12000 大型国际会议6000-9000 8000-12000 12000-16000

浙江杭州小语种翻译公司报价

加快实施“走出去”战略是适应全球化新形势和我国发展新变化，培育参与和引领国际合作和竞争新优势的重要举措。据预测，今后五年，我国对外投资规模总量超过5000亿美元，并且年增速在10%以上。浙江是外贸大省，境外经贸合作区建设走在全国前列，境外投资一直保持高速增长，《浙江省利用外资和境外投资“十三五”规划》也作出了明确部署。跨境法商论坛拟计划在杭州举办，将促进浙企与马来西亚、新加坡相关机构的直接对话，帮助浙江企业进一步拓展“一带一路”市场，寻找国际合作渠道，促进有效投资。 各式各样大手笔的贸易投资合作，也预示着新的发展机会。对从事语言服务工作的人士无疑是好消息。据中青在线记者报道，在之前“一带一路”国际合作高峰论坛会议中，现场的同传耳机里，18种工作语言分别是：汉语、英语、法语、俄语、西班牙语、柬埔寨语、捷克语、匈牙利语、印度尼西亚语、哈萨克语、老挝语、蒙古语、波兰

语、塞尔维亚语、土耳其语、越南语、日语和韩语。每个座位上都放有一张列举了这些语言的名单，除了标注与同传耳机频道对应的16种语言以外，同传耳机中的第17、第18频道分别是日语和韩语。 这无疑是翻译从业者的一剂强心针，不少小语种从业者和学习者表示，政府、学校、企业等对于小语种的关注度，现在越来越高了。更日常的商务沟通、贸易合作等等势必越来越密集和频繁，毫无疑问，国内的翻译人才供不应求，高质量的翻译人群，已经成为最抢手的人才。 随着翻译需求的不断加大，国内的翻译产业开始蓬勃发展。从2012年到2015年，我国翻译专业硕士(MTI)学位授予点也由2007年的15所大学增加至2016年的215所大学，国内翻译公司数量已达到72，485家。咱们先了解一下市场小语种的翻译报价参考： *以上报价为人民币基准价，不含税金，仅供参考，具体报价根据需译资料数量、领域、难易等具体确定！

中译英翻译报价单中译英翻译价格

精诚翻译公司五周年五折优惠中5年经验！先翻译后付费学生客户送50元优惠券，可以搜索精诚翻译公司者50元翻译找到我们 The book of“Chinese Language" aims at improving students' Chinese accomplishment and emphasizes on humanity, instead of literature or humanism. The book mainly consists of literary works, and also involves philosophy, history, art, science and technology, so as to interest students of different majors and help broaden their vision. 1Ancient literature 2 Modern literature 3 English-Chinese translation In the textbook of Public English, one third of contents have been updated, therefore, the contents become more interesting, comprehensive and practical. The attached vocabularies enable students to master the law of learning vocabularies, and the actual use of English sentences help improve their ability of using English. "Fundamentals of Management" is a subject which discusses basic theories, principles, management functions and general method of management activities, it also combines theories with practice closely. Through studying this course, students should be familiar with basic concept of management, relevant knowledge system and thoughts by various management school; understanding basic management theories and relevant principles in depth, as well as planning, decision-making, organization, leadership, motivation, control, communication and other basic management functions and methods. "The History of Chinese Culture" The book' author is an contemporary Chinese culture expert who has published many cultural works. This book focuses on evolution of academic thought and culture, at the same time, it also consider behavior, system,

山东青岛小语种翻译公司报价

“一带一路”倡议提出五年来，青岛市紧紧围绕“新亚欧大陆桥经济走廊主要节点城市”和“海上合作战略支点”功能定位，积极融入大局，深入贯彻国家政策，在经贸合作、外事外宣、金融保障、海洋科技合作等领域着力打造对外开放新高地。对“一带一路”沿线国家累计投资69.8亿美元，承包工程完成营业额130.6亿美元。全市银行机构累计为“一带一路”沿线国家和地区有投资项目的84家大型企业授信860.3亿元，贷款余额445.1亿元，支持3000余家企业与“一带一路”沿线61个国家开展贸易投资与建设合作。市级领导出访沿线国家达50余批次；接待国外重要来宾、团组来访530余批次，友城总数达到70个，遍及全球37个国家。 各式各样大手笔的贸易投资合作，也预示着新的发展机会。对从事语言服务工作的人士无疑是好消息。据中青在线记者报道，在之前“一带一路”国际合作高峰论坛会议中，现场的同传耳机里，18种工作语言分别是：汉语、

英语、法语、俄语、西班牙语、柬埔寨语、捷克语、匈牙利语、印度尼西亚语、哈萨克语、老挝语、蒙古语、波兰语、塞尔维亚语、土耳其语、越南语、日语和韩语。每个座位上都放有一张列举了这些语言的名单，除了标注与同传耳机频道对应的16种语言以外，同传耳机中的第17、第18频道分别是日语和韩语。 这无疑是翻译从业者的一剂强心针，不少小语种从业者和学习者表示，政府、学校、企业等对于小语种的关注度，现在越来越高了。更日常的商务沟通、贸易合作等等势必越来越密集和频繁，毫无疑问，国内的翻译人才供不应求，高质量的翻译人群，已经成为最抢手的人才。 随着翻译需求的不断加大，国内的翻译产业开始蓬勃发展。从2012年到2015年，我国翻译专业硕士(MTI)学位授予点也由2007年的15所大学增加至2016年的215所大学，国内翻译公司数量已达到72，485家。咱们先了解一下市场小语种的翻译报价参考： *以上报价为人民币基准价，不含税金，仅供参考，具体报价根据需译资料数量、领域、难易等具体确定！ 尽管翻译人才输出与翻译机构成立都发展迅速，但真正能满足企业发展需求的高质量翻译机构却并不好找。一方面是因为从事翻译行业的，不少都是翻译新手，没有行业经验和过硬实力，另一方面，也是因为翻译机构资质参差不齐，没有统一的规范，翻译价格和翻译质量也受到影响。怎么选择靠谱的翻译机构就成为企业的困惑点。

小语种翻译现状

小语种翻译现状 目前很多大城市会出现一种奇怪的现象，当小众语种国家人代表在我国开会发言演讲时，台下的大家只能眼巴巴的望着他却不知所云，居然没人能翻译，这种现象引起了各相关部门的广泛关注。翻译达人表示说，我国很多二三线城市同声传译人才缺乏，翻译机构规模档次不够。面对二三线城市建设步伐的加快以及国际性会议的增多，高端翻译市场亟待提升档次。 国际会议尴尬 西安高新区工作的张先生讲述到，某次会议当天，来自亚洲的一些国家的部门代表轮流发言，参与会议的也都是来自周边国家的企业以及政府代表。每人配备同声传译设备，并且有同传人员现场翻译，一切看上去井井有条。可当轮到格鲁吉亚一位代表发言时，同传人员却“撤退”了。说着格鲁吉亚语的这位代表只好自顾自说了半天，下面参会人员看上去一片茫然。 人才严重匮乏 目前大多二三线城市的小语种翻译人员都是从北京、上海、广州这些大城市请过来的，并且价格不菲！同声传译人才对翻译水平的要求最高，不仅要具备良好的口语功底，还要对当地的文化有所了解，一般都需要有国外生活几年的经历才能胜任。大多二三线城中外语翻译人才还仅仅停留在英语方面，小语种翻译人才严重匮乏。而能提供大多小语种翻译的，一般只有像翻译达人这样的翻译平台。 小语种翻译专业开设少 导致小语种翻译人才稀缺的因素有很多，其中有一个因素就是开设小语种专业的高校少。比如小语种罗马尼亚语，全国仅有1所大学开设了这个专业，即北京外国语大学。还有上文提到的格鲁吉亚语，目前在我国还没有一所大学开设了

这个专业。曾经北大给俄语专业的学生开设了这个课程，请的格鲁吉亚的外教讲授的，但是因为外教的变动，这课程现在也没有了。因为开设小语种的学校少，学习该语种的人自然也少。随之就是翻译的价格水涨船高。可以说，翻译人才越难找，收费也就越贵。 翻译市场亟待壮大 人才的匮乏会明显的限制整个翻译市场的壮大与发展，国际性会议的大幅度增多，更导致了小语种人才严重稀缺。而懂得小语种的翻译人才，目前正在成为各大公司热捧的对象。甚至因为人才稀缺，企业在招聘标准上也低出不少，如某些公司招聘负责商务谈判及日常翻译工作的俄语翻译，已经打出“应届毕业生也可”的条件。所以，目前我国的小语种翻译市场亟待扩大，也需要更多的小语种翻译人才。