arXiv subjects

P. D. Gujrati

Publications and source records attributed to P. D. Gujrati.

At least 19 recordsLinked to original sources

arXiv2024

A No-Go Theorem of Analytical Mechanics for the Second Law Violation

We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to solve a long-standing problem of identifying the underlying cause of the second law (SL) of spontaneous irreversibility, a stochastic universal principle, as the mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics of an isolated nonequilibrium system of any size. The principle leads to nonnegative system intrinsic (SI) microwork and SI-average macrowork dW during any spontaneous process. In conjuction with the first law, Mec-EQ-P leads to a generalized second law (GSL) dQ=dW>0, where dQ=TdS is the purely stochastic SI-macroheat that corresponds to dS>0 for T>0 and dS<0 for T<0, where T is the temperature. The GSL supercedes the conventional SL formulation that is valid only for a macroscopic system for positive temperatures temperatures, but reformulates it to dS<0 for negative temperatures. It is quite surprising that GSL is not only a direct consequence of intertwined mechanical and stochastic macroquantities through the first law but also remains valid for any arbitrary irreversible process in a system of any size as an identity for positive and negative temperatures. It also becomes a no-go theorem for GSL-violation unless we abandon Mec-EQ-P of analytical mechanics used in the BCM proposal, which will be catastrophic for theoretical physics. In addition, Mec-EQ-P also provides new insights into the roles of spontaneity, nonspontaneity, negative temperatures, instability, and the significance of dS<0 due to nonspontaneity and inserting internal constraints.

cond-mat.stat-mech↗

arXiv2022

Maxwell's Conjecture of the Demon creating a Temperature Difference is False

We argue that Maxwell's demon is incapable of creating a nonzero temperature difference. Hence, it does not destroy equilibrium and the second law is never at risk, contrary to the claim by Maxwell and accepted by many. It is therefore remarkable that despite this, the demon paradox has been a valuable source of new ideas. We use two independent arguments, one using classical equilibrium thermodynamics by extending Brillouin's approach, and the other one using equilibrium statistical mechanics and the central limit theorem.

cond-mat.stat-mech↗

arXiv2022

Overlooked Work and Heat of Intervention and the Fate of Information Principles of Szilard and Landauer

We show that any external intervention (insertion or removal of a partition) that destroys the equilibrium or brings it in a system always requires work and heat to ensure that the first law is obeyed, a fact that has been completely overlooked in the literature. As a consequence, there is no second law violation. We discuss the ramifications of our finding for information principles of Szilard and Landauer and show that no information entropy is needed. The relevance of this result for Maxwell's demon is also considered.

physics.class-ph↗

arXiv2021

Maxwell's Demon must remain sebservient to Clausius's statement

Using classical thermodynamics, we argue that Maxwell's demon loses its battle against Clausius as any temperature difference or other thermodynamic forces it creates is immediately compensated by spontaneous counterbalancing flows that bring about equilibration by slower particles in principle. Being constrained by these spontaneously generated equilibration processes in which he actively but unwittingly participates, the demon is incapable of destroying equilibrium and violating the second law. In fact, our investigation shows that he is unintentionally designed to support it, and does not alter the temperature.

physics.class-ph↗

arXiv2021

Nonequilibrium Entropy in an Extended State Space

This chapter deals with our recent attempt to extend the notion of equilibrium (EQ) entropy to nonequilibrium (NEQ) systems so that it can also capture memory effects. This is done by enlarging the equilibrium state space by introducing internal variables. These variables capture the irreversibility due to internal processes. By a proper choice of the enlarged state space, the entropy becomes a state function, which shares many properties of the EQ entropy, except for a nonzero irreversible entropy generation. We give both a thermodynamic and statistical extension of the entropy and prove their equivalence in all cases by taking an appropriate state space. This provides a general nonnegative statistical expression of the entropy for any situation. We use the statistical formulation to prove the second law. We give several examples to determine the required internal variables, which we then apply to several cases of interest to calculate the entropy generation. We also provide a possible explanation for why the entropy in the classical continuum 1-d Tonks gas can become negative by considering a lattice model for which the entropy is always nonnegative.

cond-mat.stat-mech↗

arXiv2021

A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications

The review deals with a novel approach (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space involving internal variables as additional state variables. The IEQ-macrostates are unique in the enlarged state space and have no memory just as EQ macrostates are in the EQ state space. The approach provides a clear strategy to identify the internal variables for any model through several examples. The MNEQT deals directly with system-intrinsic quantities, which are very useful as they fully describe irreversibility. Because of this, MNEQT solves a long-standing problem in NEQT of identifying a unique global temperature T of a system, thus fulfilling Planck's dream of a global temperature for any system, even if it is not uniform such as when it is driven between two heat baths; T has the conventional interpretation of satisfying the Clausius statement that the exchange macroheat flows from hot to cold, and other sensible criteria expected of a temperature. The concept of the generalized macroheat dQ converts the Clausius inequality into the Clausius equality dS=dQ/T, which also covers macrostates with memory, and follows from the extensivity property. The equality also holds for a NEQ isolated system. The novel approach is extremely useful as it also works when no internal state variables are used to study nonunique macrostates in the EQ state space at the expense of explicit time dependence in the entropy that gives rise to memory effects. To show the usefulness of the novel approach, we give several examples such as irreversible Carnot cycle, friction and Brownian motion, the free expansion, etc.

cond-mat.stat-mech↗

arXiv2021

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

We extend and successfully apply a recently proposed microstate nonequilibrium thermodynamics to study expansion/contraction processes. Here, the numbers of initial and final microstates are different so they cannot be connected by unique Hamiltonian trajectories. This commonly happens when the phase space volume changes, and has not been studied so far using Hamiltonian trajectories that can be inverted to yield an identity mapping between initial and final microstates as the parameter in the Hamiltonian is changed. We propose a trick to overcome this hurdle with a focus on free expansion in an isolated system, where the concept of dissipated work is not clear. The trick is shown to be thermodynamically consistent and can be extremely useful in simulation. We justify that it is the thermodynamic average of the internal microwork done by a microstate that is dissipated; this microwork is different from the exchange microwork with the vacuum, which vanishes. We also establish that the microwork is nonnegative for free expansion, which is remarkable, since its sign is not fixed in a general process.

cond-mat.stat-mech↗

arXiv2020

A First-Principles Nonequilibrium Deterministic Equation of Motion of a Brownian Particle and Microscopic Viscous Drag

We present a first-principles thermodynamic approach to provide an alternative to the Langevin equation by identifying the deterministic (no stochastic component) microforce F_{k,BP} acting on a nonequilibrium Brownian particle (BP) in its kth microstate m_{k}. (The prefix micro refers to microstate quantities and carry a suffix k.) The deterministic new equation is easier to solve using basic calculus. Being oblivious to the second law, F_{k,BP} does not always oppose motion but viscous dissipation emerges upon ensemble averaging. The equipartition theorem is always satisfied. We reproduce well-known results of the BP in equilibrium. We explain how the microforce is obtained directly from the mutual potential energy of interaction beween the BP and the medium after we average it over the medium so we only have to consider the particles in the BP. Our approach goes beyond the phenomenological and equilibrium approach of Langevin and unifies nonequilibrium viscous dissipation from mesoscopic to macroscopic scales and provides new insight into Brownian motion beyond Langevin's and Einstein's formulation.

cond-mat.stat-mech↗

arXiv2020

Comment on "The generalized Boltzmann distribution is the only distribution in which the Gibbs-Shannon entropy equals the thermodynamic entropy" by X. Gao, E. Gallicchio and A.E. Roitberg [J. Chem. Phys. 151, 034113 (2019)]

The title of the paper leads to an incorrect conclusion as we show that the equilibrium result of the paper is a special limit of a general result for nonequilibrium systems in internal equilibrium already available in the literature. We also point out some of the limitations of the approach taken by the authors.

physics.chem-ph↗

arXiv2019

Jensen Inequality and the Second Law

Jensen's Inequality (JIEQ) has proved to be a major tool to prove the consistency of various fluctuation theorems with the second law in microscopic thermodynamics. We show that the situation is far from clear and the reliance on the JIE may be quite misleading in general.

cond-mat.stat-mech↗

arXiv2019

Consequences of the Detailed Balance for the Crooks Fluctuation Theorem

We show that the assumptions of the detailed balance and of the initial equilibrium macrostate, which are central to the Crooks fluctuation theorem (CFT), lead to all microstates along a trajectory to have equilibrium probabilities. We also point out that the Crooks's definition of the backward trajectory does not return the system back to its initial microstate. Once corrected, the detailed balance assumption makes the CFT a theorem only about reversible processes involving reversible trajectories that satisfy Kolmogorov's criterion. As there is no dissipation, the CFT cannot cover irreversible processes, which is contrary to the common belief. This is consistent with our recent result that the JE is also a result only for reversible processes.

cond-mat.stat-mech↗

arXiv2019

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

We present a novel hybrid but thermodynamic approach to provide an alternative to the Langevin equation by using system-intrinsic (SI) microwork done by the Brownian particle in the kth microstate (realization). The corresponding SI-microforce is unique to the microstate and determines the microscopic equation of motion for it. Being a thermodynamic approach, the equipartition theorem is always satisfied and no additional stochastic Langevin force is needed. We determine instantaneous and long-time averages of useful quantities and thus provide a new unified approach to the fluctuating motion from mesoscopic to macroscopic scales.

cond-mat.stat-mech↗

arXiv2018

Correcting the Mistaken Identification of Nonequilibrium Microscopic Work

The energy change dE_k for the kth microstate is erroneously equated with the external work done on the microstate. It ignores the ubiquitous internal energy change d_iW_k due to force imbalance between the internal and external forces. We show that this contribution is present even in a reversible process, which is a surprise. We show that the correct identification is dE_k=-dW_k, where dW_k is the generalized work done by the microstate. We prove that the thermodynamic average of the internal work gives dissipation and is not captured by the external work. The latter effectively sets d_iW_k =0 and results in no dissipation. Using dW_k to account for irreversibility, we obtain a new work relation that works even for free expansion, where the Jarzynski equality fails. In the new work relation, dW_k depends only on the energies of the initial and final states and not on the actual process. This makes the new relation very different from the Jarzynski equality. The correction has far-reaching consequences and requires reassessment of current applications of external work in theoretical physics.

cond-mat.stat-mech↗

arXiv2018

Hierarchy of Relaxation times and Residual Entropy: A Nonequilibrium Approach

We consider nonequilibrium (NEQ) states such as supercooled liquids and glasses that are described with use of internal variables. We classify the latter by state-dependent hierarchy of relaxation times to assess their relevance for irreversible contributions. Given an observation time τ_{obs}, we determine the window of relaxation times that divide the internal variables into active and inactive groups, the former playing a central role in the NEQ thermodynamics. Using this thermodynamics, we determine (i) a bound on the NEQ entropy and on the residual entropy, and (ii) the nature of isothermal relaxation of the entropy and the enthalpy in accordance with the second law. A theory that violates the second law such as the entropy loss view is shown to be internally inconsistent if we require it to be consistent with experiments. The inactive internal variables still play an indirect role in determining the temperature T(t), the pressure P(t), of the system, which deviate from their external values.

cond-mat.stat-mech↗

arXiv2018

The Role of the Communal Entropy and Free Volume for the Viscosity Divergence near the Glass Transition: A New Conceptual Approach

The conventional approach to study glasses either requires considering the rapid drop in the excess entropy ΔS_ex or the free volume V_f. As the two quantities are not directly related to each other, the viscosity in the two approaches do not diverge at the same temperature, which casts doubt on the physical significance of the divergence and of the ideal glass transition (IG). By invoking a recently developed nonequilibrium thermodynamics, we identify the instantaneous temperature, pressure, entropy, etc. and discover the way they relax. We show that by replacing ΔS_ex by a properly defined communal entropy S^comm (not to be confused with the configurational entropy) and V_f vanish simultaneously at IG, where the glass is jammed with no free volume and communal entropy. By exploiting the fact that there are no thermodynamic singularities in the entropy of the supercooled liquid at IG, we show that various currently existing phenomenologies become unified.

cond-mat.stat-mech↗

arXiv2018

Jarzynski Equality and its Special Trajectory Ensemble Average Demystified

The special trajectory ensemble average (TEA), denoted by a subscript 0, in the Jarzynski Equality (JE) results in the Jensen inequality _0 GT-EQ delta(F) for the work R done on the system, and not the thermodynamic work inequality GT-EQ delta(F) since we find NEQ _0. Therefore, contrary to the common belief, the Jensen inequality does not directly support the JE as a nonequilibrium result. Jarzynski's microscopic treatment of the inclusive energy considers only the external work d_eE_k but neglects the ubiquitous change d_iE_k due to external-internal force imbalance, though d_iE_k's are present even in a reversible process as we show. Because of this neglect, no thermodynamic force necessary for dissipation is allowed. Thus the JE has no built-in irreversibility, despite a time-dependent work protocol. We support our claim by an explicit calculation, which shows that _0 > delta(F) even for a reversible process for which = delta(F). This also confirms that and _0 are different averages.

cond-mat.stat-mech↗

arXiv2017

Comment on Ben-Amotz and Honig, "Average entropy dissipation in irreversible mesoscopic processes," Phys. Rev. Lett. 96, 020602 (2006)

We point out that most of the classical thermodynamics results in the paper have been known in the literature, see Kestin and Woods, for quite some time and are not new, contrary to what the authors imply. As shown by Kestin, these results are valid for quasistatic irreversible processes only and not for arbitrary irreversible processes as suggested in the paper. Thus, the application to the Jarzynski process is limited.

physics.chem-ph↗

arXiv2017

Nonequilibrium Work and its Hamiltonian Connection for a Microstate in Nonequilibrium Statistical Thermodynamics: A Case of Mistaken Identity

Nonequilibrium work-Hamiltonian connection for a microstate plays a central role in diverse branches of statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.). We show that the change in the Hamiltonian for a microstate should be identified with the work done by it, and not the work done on it. This contradicts the current practice in the field. The difference represents a contribution whose average gives the work that is dissipated due to irreversibility. As the latter has been overlooked, the current identification does not properly account for irreversibilty. As an example, we show that the corrected version of Jarzynski's relation can be applied to free expansion, where the original relation fails. Thus, the correction has far-reaching consequences and requires reassessment of current applications.

cond-mat.stat-mech↗