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To describe the nonequilibrium states of a system, we introduce a new thermodynamic parameter—the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a system by specifying the stochastic processes are written down. The change in the lifetime values by interaction with environment is expressed in terms of fluxes and sources. The expressions for the nonequilibrium entropy, temperature, and entropy production are obtained, which at small values of fluxes coincide with those derived within the frame of extended irreversible thermodynamics. The explicit expressions for the lifetime of a system and its thermodynamic conjugate are obtained.

In papers [

Characterizing the nonequilibrium state by means of an additional parameter related to the deviation of a system from the equilibrium (field of gravity, electric field for dielectrics, etc.) was used in [

The characteristics of

The shape of the potential of a system

The major part of the living time the system dwells within the vicinity of the point

The lifetime seems to be a value of more general character than the fluxes are (this fact being the prerequisite of formulating a theory which would include the EIT as its partial case) and, moreover, it seems to be more conservative (that is, the lifetime in this respect stands closer to the ordinary conserving values). The history of a system is the succession of repeating “busy periods”—lifetimes in the sense of the definition (

Very close to the scope of the present work stand the papers [

In the present paper, we provide the statistical foundations for the thermodynamic relations and introduce the distribution for the lifetime of a system (Section

Let us consider a macroscopic observable

The standard procedure (e.g., [

Now we make an assumption about the form of

We did not concretize yet the parameter

The linearity of the exponent in (

From the expressions (

Let us choose some reference point

The value

If

Let us suppose that the process

The values

As we note in Conclusion, the structure factor

We have from (

Let us introduce the nonequilibrium entropy corresponding to the distribution (

Substituting into (

Now we determine the explicit form for

Geokinetic plateau model.

The volume element of the size

Outcoming flux

The same result (

For this purpose, we will recall the expressions of the EIT [

From (

The behaviour of a system depends on its finite size, since we consider the systems with finite lifetime and finite volumes without performing the thermodynamic limit transition.

Consider now the stability of the thermodynamic system. To ensure its stability, the condition

Determining in (

Comparing entropy production

Above we considered the lifetime as a quantity related to the heat in a system. Since the heat transfer in a body is accompanied by the processes of deformation of a continuous medium, the energy dissipation is conditioned not only by the heat transfer, but by the internal friction of a system which is represented by the dissipative part of the stress tensor; thus the full expression for

In the examples considered above, one took for

If we substitute

We suppose that the expressions (

The expression for the entropy thus has a form

The assumption about the physical systems living for a finite period of time which was the starting point of the exposed here theory allows one to get the mesoscopic theory of the stationary nonequilibrium states at any deviation from the equilibrium. For the method applied, it is essential to have the relation of

Let us underline the principal features of the suggested approach.

(1) We introduce a novel variable

(2) We suppose that thermodynamic forces

(3) We suppose that a “refined” structure factor

(4) It is supposed that at least for certain classes of influences the resulting distribution has the form (

(5) The values

If one integrates (

Essential assumption is that the values

The lifetime (or escape time if one refers to the terminology of [

If one compares the exposed thermodynamics with EIT, following differences can be outlined.

(1) Different expressions for the nonequilibrium temperature, entropy

(2) A new variable of the system size is introduced which should play certain part in the nonequilibrium case. For the continuous description, this might be the size of the “continuous medium point” [

(3) Explicit expressions for the lifetime

Let the process

The forward kinetic equation for the distribution density

The Laplace transform gives the equation for

One can represent an open thermodynamic system as evolving in a random medium whose mathematical model will be either Markoff renewal processes or semi-Markoff processes. The local characteristics of the system depend on the random medium state. The scheme of the asymptotic phase coarsening present the simplified description of the system evolution in a random medium which can be performed based upon a simple set of heuristic rules [

In our case, the stationary distributions are described by the Gibbs distributions. Absorbing state is the degenerated state of the system with