Generalized Non-equilibrium Heat and Work and the Fate of the Clausius Inequality

Abstract

By generalizing the traditional concept of heat dQ and work dW to also include their time-dependent irreversible components diQ and diW allows us to express them in terms of the instantaneous internal temperature T (t) and pressure P (t), whereas the conventional form uses the constant values T0 and P0 of the medium. This results in an extremely useful formulation of non-equilibrium thermodynamics so that the first law turns into the Gibbs fundamental relation and the Clausius inequality becomes an equality dQ(t)/T (t) ≡ 0 in all cases, a quite remarkable but unexpected result. We determine the irreversible components diQ ≡ diW and discuss how they can be determined to obtain the generalized dW (t) and dQ(t).

A Novel Trick to Overcome the Phase Space Volume Change and the Use of Hamiltonian Trajectories with an emphasis on the Free Expansion

“…In conclusion, it is not a surprise that we are left to exclusively use the MNEQT and µNEQT in this study of interacting and isolated systems. We have already applied the MNEQT to briefly study free expansion [42,43]. Here, we wish to go beyond the earlier study to demonstrate how the µNEQT can be used to study expansion/contraction with special attention to free expansion by including internal variables also.…”

“…(14b). As {p k } is not changed in dE w , it is evaluated at fixed entropy S [16,42]. Comparing dE with the first law in Eq.…”

Hybrid Einstein-Langevin Approach for Microscopic formulation of Viscous Drag: An Alternative to the Langevin Equation

“…We will treat the piston problem for simplicity as it is commonly discussed in introductory physics. Let x denote a phase point in the phase space of Σ so that the Hamiltonian of the system is written as H( x| V, P BP , P R ) in which V, P BP and P R appear as parameters: the variations dV, dP BP and dP R change the value of H; this change represents the generalized work dW done by the system as shown elsewhere [25][26][27][28][29][30][31]. Introducing the system-intrinsic (SI) "mechanical forces" obtained directly from the SI-Hamiltonian…”

Determination of Nonequilibrium Temperature and Pressure using Clausius Equality in a State with Memory: A Simple Model Calculation

“…background Recently, we have proposed [18][19][20][21][22] a definition of the nonequilibrium temperature, pressure, etc. for a nonequilibrium system that is in internal equilibrium; the latter requires introducing internal variables ξ as additional state variables that become superfluous in the equilibrium state.…”

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