Thermodynamics and an Introduction to Thermostatistics

Callen, H. B. (1985). Thermodynamics and an Introduction to Thermostatistics. Wiley.

Type

Book

Intellectual base

Textbook

Year

1985

ISBN

9780471862567

Link

https://www.wiley.com/en-us/Thermodynamics+and+an+Introduction+to+Thermostatistics%2C+2nd+Edition-p-9780471862567

Cited from

economics_finance, information_theory, mathematics, physics

Cited by

14 citations across 13 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Comparative Statics
  • This is the same complexity-management move that makes equilibrium thermodynamics tractable: state functions of a system at equilibrium are well-defined and manipulable even when the underlying microscopic dynamics are chaotic and unsimulable.

    This sourceStandard reference on equilibrium thermodynamics, where state functions are well-defined despite chaotic microscopic dynamics; develops Le Chatelier's principle. (

    Supported in partVerified against the publisher's abstract

    Publisher abstract for a standard equilibrium-thermodynamics textbook; it confirms the macroscopic, self-contained treatment of thermodynamics but says nothing about state functions under chaotic, unsimulable microscopic dynamics.

    “The only text to cover both thermodynamic and statistical mechanics--allowing students to fully master thermodynamics at the macroscopic level.”

    Read by an automated reader; not a human review. How support was checked

• Convexity
  • The transferable content of convexity is a set of structural diagnostics and inequalities that carry across substrates because each attaches to the second-order shape of the objects under combination rather than to any field. Optimization transfers into policy design: knowing that local incentives suffice to reach a global optimum when the welfare function is concave tells a policymaker when decentralized markets will reach a global optimum and when they will not, and the structural diagnostic — is the joint feasible set convex? — predicts whether decentralization can succeed. Statistics transfers into diagnosis: identifying that a model's maximum-likelihood objective is non-convex is a transferable warning that estimation will be sensitive to initialization, that local optima may be reported as global, and that re-parameterization may help, and the identical warning applies in economic estimation, psychometric fitting, and deep-learning training. Probability transfers into forecasting: Jensen's inequality is the structural reason the average of forecasts differs from the forecast of the average, with the direction of the gap set by the convexity of the transformation, and this transfers immediately into pricing, risk measurement, and aggregate-versus-individual prediction. Geometry transfers into ethics and fair division: the convex hull of individual options is the set of feasible compromises, so a randomized compromise that no party would individually pick may dominate any pure compromise, a fact directly usable in bargaining, voting, and allocation. Thermodynamics transfers into economics: the common-tangent construction that resolves a non-convex free energy into a two-phase mixture is the same convexification that turns a non-convex production set into two-firm specialization rather than one mid-scale firm.

    This sourceConvexity of thermodynamic potentials and the common-tangent construction resolving a non-convex free energy into a stable two-phase mixture.

• Reversibility and Irreversibility
  • The prime asks: "What is the cost of undoing this, and who bears it?" not "What are the deep thermodynamic reasons?"—the latter being the domain Callen (1985) treats axiomatically through entropy and the Second Law in his canonical thermodynamics text.

    This sourceModern axiomatic treatment of thermodynamics based on variational principles (entropy maximum, free-energy minimum) for characterizing equilibrium; establishes equilibrium as the consequence of constrained optimization, providing pedagogical clarity on why equilibrium takes on specific mathematical form.

    Supported in partVerified against the publisher's abstract

    The publisher abstract confirms Callen 1985 is a canonical macroscopic-thermodynamics textbook, but says nothing about an 'axiomatic' treatment through entropy and the Second Law.

    “The only text to cover both thermodynamic and statistical mechanics--allowing students to fully master thermodynamics at the macroscopic level.”

    Read by an automated reader; not a human review. How support was checked

• Thermodynamic Equilibrium
  • Every thermodynamic-equilibrium articulation specifies (1) the system and its constraints — isolated (microcanonical: fixed E, V, N), in thermal contact with a reservoir (canonical: fixed T, V, N), or exchanging matter (grand canonical: fixed T, V, μ); (2) the equilibrium conditions — uniform temperature (thermal equilibrium), uniform pressure (mechanical equilibrium), uniform chemical potentials of each species (chemical equilibrium), no unbalanced forces or flows

    This sourceModern axiomatic treatment of thermodynamics based on variational principles (entropy maximum, free-energy minimum) for characterizing equilibrium; establishes equilibrium as the consequence of constrained optimization, providing pedagogical clarity on why equilibrium takes on specific mathematical form.

• Transformation
  • A mathematician reasoning about eigenvalues and eigenvectors ("directions that are preserved by a linear transformation") reasons similarly to a biologist reasoning about developmental invariants ("cell lineages that maintain identity through morphogenesis"), or to a thermodynamicist reasoning about phase change, which Callen (1985) formalizes as a transformation between equilibrium states governed by conserved extensive variables.

    This sourceModern axiomatic treatment of thermodynamics based on variational principles (entropy maximum, free-energy minimum) for characterizing equilibrium; establishes equilibrium as the consequence of constrained optimization, providing pedagogical clarity on why equilibrium takes on specific mathematical form.

Domain-specific

• Isolated System
  • The system's total energy is consequently conserved in the nonrelativistic thermodynamic treatment, and its matter content remains fixed unless mass-energy conversion is explicitly part of the model

    This sourceCallen's postulational treatment carries the conservation itself — internal energy is a conserved extensive parameter, and a wall restrictive to energy, volume and all mole numbers fixes energy and matter content together; the nonrelativistic restriction is not his, Chapter 1 recording instead that Einstein extended energy conservation to the relativistic region. Callen's entropy-maximum postulate, with the quasi-static and reversible processes of his Chapter 4: releasing an internal constraint in a system with restrictive walls raises the entropy, and only reversible evolution leaves it unchanged.

    Supported in partVerified against the source

    Read by an automated reader; not a human review. How support was checked

• Isothermal Process
  • “Isothermal” fixes one state variable; it does not determine every other coordinate or transfer.
• Principle of minimum energy
  • The principle of minimum energy states that stable equilibrium minimizes internal energy under fixed entropy and fixed external constraints.
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Spontaneous process
  • … and pressure or volume constraints, relevant thermodynamic potential, sign convention, free-energy or total-entropy criterion, equilibrium direction and kinetic distinction are explicit. to An applied instance preserves the same invariant under changed scale, notation, dataset, jurisdiction, or implementation..
• State function
  • Internal energy, entropy and state coordinates are state functions while heat and work are path quantities; exact differentials, equilibrium assumptions and composition constraints determine applicability.
• State variable
  • … because their current values and applied force determine subsequent motion under the differential equations. to In thermodynamics, a selected set such as pressure and temperature can determine an equilibrium simple compressible system's state only within the applicable equation-of-state and phase conditions..
• Van der Waals Equation
  • It explains why finite volume and attraction alter ideal behavior and provides a tractable model of liquid-gas continuity.

Mechanisms

• Carnot or Theoretical-Limit Benchmark
  • Its central failure mode is that the ceiling is only a ceiling — reversible operation requires infinitely slow, infinitely large equipment, so the bound is unreachable by construction and a naive reader treats a real plant as a failure for not hitting it.

    This sourcePresents Carnot efficiency as an unattainable upper bound requiring ideal reversible operation rather than a practical plant target.

Verification

Does it exist? Confirmed. This work's ISBN resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Read against the text for 3 of 14 citations: 3 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://www.wiley-vch.de/en/areas-interest/engineering/mechanical-engineering-10me/thermodynamics-10me2/thermodynamics-and-an-introduction-to-thermostatistics-978-0-471-86256-7 ×1

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